All Issues

Volume 23, 2018

Volume 22, 2017

Volume 21, 2016

Volume 20, 2015

Volume 19, 2014

Volume 18, 2013

Volume 17, 2012

Volume 16, 2011

Volume 15, 2011

Volume 14, 2010

Volume 13, 2010

Volume 12, 2009

Volume 11, 2009

Volume 10, 2008

Volume 9, 2008

Volume 8, 2007

Volume 7, 2007

Volume 6, 2006

Volume 5, 2005

Volume 4, 2004

Volume 3, 2003

Volume 2, 2002

Volume 1, 2001

Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.

DCDS-B is edited by a global community of leading scientists to guarantee its high standards and a close link to the scientific and engineering communities. A unique feature of this journal is its streamlined review process and rapid publication. Authors are kept informed at all times throughout the process through the rapid, direct and personal communication between the authors and editors.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 10 issues a year in January, March, May, June, July, August, September, October, November and December.
  • Publishes both online and in print.
  • Indexed in Science Citation Index, ISI Alerting Services, CompuMath Citation Index, Current Contents/Physics, Chemical, & Earth Sciences, INSPEC, Mathematical Reviews, MathSciNet, PASCAL/CNRS, Scopus, Web of Science and Zentralblatt MATH.
  • Archived in Portico and CLOCKSS.
  • DCDS-B is a publication of the American Institute of Mathematical Sciences. All rights reserved.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

Select all articles


Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity
Zhenguo Bai and Tingting Zhao
2018, 23(10) : 4063-4085 doi: 10.3934/dcdsb.2018126 +[Abstract](644) +[HTML](433) +[PDF](519.85KB)

A non-local delayed reaction-diffusion model with a quiescent stage is investigated. It is shown that the spreading speed of this model without quasi-monotonicity is linearly determinate and coincides with the minimal wave speed of traveling waves.

Time asymptotics of structured populations with diffusion and dynamic boundary conditions
Mustapha Mokhtar-Kharroubi and Quentin Richard
2018, 23(10) : 4087-4116 doi: 10.3934/dcdsb.2018127 +[Abstract](555) +[HTML](360) +[PDF](467.24KB)

This work revisits and extends in various directions a work by J.Z. Farkas and P. Hinow (Math. Biosc and Eng, 8 (2011) 503-513) on structured populations models (with bounded sizes) with diffusion and generalized Wentzell boundary conditions. In particular, we provide first a self-contained \begin{document}$L^{1}$\end{document} generation theory making explicit the domain of the generator. By using Hopf maximum principle, we show that the semigroup is always irreducible regardless of the reproduction function. By using weak compactness arguments, we show first a stability result of the essential type and then deduce that the semigroup has a spectral gap and consequently the asynchronous exponential growth property. Finally, we show how to extend this theory to models with arbitrary sizes and point out an open problem pertaining to this extension.

On a free boundary problem for a nonlocal reaction-diffusion model
Jia-Feng Cao, Wan-Tong Li and Meng Zhao
2018, 23(10) : 4117-4139 doi: 10.3934/dcdsb.2018128 +[Abstract](561) +[HTML](368) +[PDF](474.87KB)

This paper is concerned with the spreading or vanishing dichotomy of a species which is characterized by a reaction-diffusion Volterra model with nonlocal spatial convolution and double free boundaries. Compared with classical reaction-diffusion equations, the main difficulty here is the lack of a comparison principle in nonlocal reaction-diffusion equations. By establishing some suitable comparison principles over some different parabolic regions, we get the sufficient conditions that ensure the species spreading or vanishing, as well as the estimates of the spreading speed if species spreading happens. Particularly, we establish the global attractivity of the unique positive equilibrium by a method of successive improvement of lower and upper solutions.

Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ)
Hebai Chen and Xingwu Chen
2018, 23(10) : 4141-4170 doi: 10.3934/dcdsb.2018130 +[Abstract](612) +[HTML](455) +[PDF](1375.03KB)

The degenerate Bogdanov-Takens system \begin{document}$\dot x = y-(a_1x+a_2x^3),~\dot y = a_3x+a_4x^3$\end{document} has two normal forms, one of which is investigated in [Disc. Cont. Dyn. Syst. B (22)2017,1273-1293] and global behavior is analyzed for general parameters. To continue this work, in this paper we study the other normal form and perform all global phase portraits on the Poincaré disc. Since the parameters are not restricted to be sufficiently small, some classic bifurcation methods for small parameters, such as the Melnikov method, are no longer valid. We find necessary and sufficient conditions for existences of limit cycles and homoclinic loops respectively by constructing a distance function among orbits on the vertical isocline curve and further give the number of limit cycles for parameters in different regions. Finally we not only give the global bifurcation diagram, where global existences and monotonicities of the homoclinic bifurcation curve and the double limit cycle bifurcation curve are proved, but also classify all global phase portraits.

On the Cauchy problem for the XFEL Schrödinger equation
Binhua Feng and Dun Zhao
2018, 23(10) : 4171-4186 doi: 10.3934/dcdsb.2018131 +[Abstract](505) +[HTML](362) +[PDF](412.45KB)

In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equation with a time-dependent electromagnetic field and a Coulomb potential, which arises as an effective single particle model in X-ray free electron lasers(XFEL). We firstly show the local and global well-posedness for the Cauchy problem under the assumption that the magnetic potential is unbounded and time-dependent, and then obtain the regularity by a fixed point argument.

A perturbed fourth order elliptic equation with negative exponent
Zongming Guo and Long Wei
2018, 23(10) : 4187-4205 doi: 10.3934/dcdsb.2018132 +[Abstract](523) +[HTML](367) +[PDF](415.14KB)

By a new type of comparison principle for a fourth order elliptic problem in general domains, we investigate the structure of positive solutions to Navier boundary value problems of a perturbed fourth order elliptic equation with negative exponent, which arises in the study of the deflection of charged plates in electrostatic actuators in the modeling of electrostatic micro-electromechanical systems (MEMS). It is seen that the structure of solutions relies on the boundary values. The global branches of solutions to the Navier boundary value problems are established. We also show that the behaviors of these branches are relatively "stable" with respect to the Navier boundary values.

Carleman estimate for solutions to a degenerate convection-diffusion equation
Chunpeng Wang, Yanan Zhou, Runmei Du and Qiang Liu
2018, 23(10) : 4207-4222 doi: 10.3934/dcdsb.2018133 +[Abstract](498) +[HTML](352) +[PDF](448.88KB)

This paper concerns a control system governed by a convection-diffusion equation, which is weakly degenerate at the boundary. In the governing equation, the convection is independent of the degeneracy of the equation and cannot be controlled by the diffusion. The Carleman estimate is established by means of a suitable transformation, by which the diffusion and the convection are transformed into a complex union, and complicated and detailed computations. Then the observability inequality is proved and the control system is shown to be null controllable.

Global stability of a diffusive and delayed HBV infection model with HBV DNA-containing capsids and general incidence rate
Ting Guo, Haihong Liu, Chenglin Xu and Fang Yan
2018, 23(10) : 4223-4242 doi: 10.3934/dcdsb.2018134 +[Abstract](596) +[HTML](409) +[PDF](1076.74KB)

The aim of this paper is to study the dynamics of a new chronic HBV infection model that includes spatial diffusion, three time delays and a general incidence function. First, we analyze the well-posedness of the initial value problem of the model in the bounded domain. Then, we define a threshold parameter \begin{document}$R_{0}$\end{document} called the basic reproduction number and show that our model admits two possible equilibria, namely the infection-free equilibrium \begin{document}$E_{1}$\end{document} as well as the chronic infection equilibrium \begin{document}$E_{2}$\end{document}. Further, by constructing two appropriate Lyapunov functionals, we prove that \begin{document}$E_{1}$\end{document} is globally asymptotically stable when \begin{document}$R_{0}<1$\end{document}, corresponding to the viruses are cleared and the disease dies out; if \begin{document}$R_{0}>1$\end{document}, then \begin{document}$E_{1}$\end{document} becomes unstable and the equilibrium point \begin{document}$E_{2}$\end{document} appears and is globally asymptotically stable, which means that the viruses persist in the host and the infection becomes chronic. An application is provided to confirm the main theoretical results. Additionally, it is worth saying that, our results suggest theoretically useful method to control HBV infection and these results can be applied to a variety of possible incidence functions presented in a series of other papers.

Upper and lower bounds for the blow-up time in quasilinear reaction diffusion problems
Juntang Ding and Xuhui Shen
2018, 23(10) : 4243-4254 doi: 10.3934/dcdsb.2018135 +[Abstract](497) +[HTML](374) +[PDF](397.38KB)

In this paper, we consider a quasilinear reaction diffusion equation with Neumann boundary conditions in a bounded domain. Basing on Sobolev inequality and differential inequality technique, we obtain upper and lower bounds for the blow-up time of the solution. An example is also given to illustrate the abstract results obtained of this paper.

Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources
Benlong Xu and Hongyan Jiang
2018, 23(10) : 4255-4266 doi: 10.3934/dcdsb.2018136 +[Abstract](482) +[HTML](333) +[PDF](378.83KB)

This paper mainly study the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient. In this model, the species are assumed to be identical except spatial resource distribution: heterogeneity vs homogeneity. It is shown that the species with heterogeneous resources distribution is always in a better position, that is, it can always invade when rare. The ratio of advection strength and diffusion rate of the species with heterogeneous distribution plays a crucial role in the dynamics behavior of the system. Some conditions of invasion, driving extinction, and coexistence are given in term of this ratio and the diffusion rate of its competitor.

Dynamics of weak solutions for the three dimensional Navier-Stokes equations with nonlinear damping
Fang Li, Bo You and Yao Xu
2018, 23(10) : 4267-4284 doi: 10.3934/dcdsb.2018137 +[Abstract](500) +[HTML](371) +[PDF](488.66KB)

The main objective of this paper is to study the existence of a finite dimensional global attractor for the three dimensional Navier-Stokes equations with nonlinear damping for \begin{document}$r>4.$\end{document} Motivated by the idea of [1], even though we can obtain the existence of a global attractor for \begin{document}$r≥ 2$\end{document} by the multi-valued semi-flow, it is very difficult to provide any information about its fractal dimension. Therefore, we prove the existence of a global attractor in H and provide the upper bound of its fractal dimension by the methods of \begin{document}$\ell$\end{document}-trajectories in this paper.

Exponential stability of an incompressible non-Newtonian fluid with delay
Linfang Liu, Tomás Caraballo and Xianlong Fu
2018, 23(10) : 4285-4303 doi: 10.3934/dcdsb.2018138 +[Abstract](524) +[HTML](400) +[PDF](591.07KB)

The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four different approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.

Finite dimensionality of global attractor for the solutions to 3D viscous primitive equations of large-scale moist atmosphere
Boling Guo and Guoli Zhou
2018, 23(10) : 4305-4327 doi: 10.3934/dcdsb.2018160 +[Abstract](299) +[HTML](245) +[PDF](457.5KB)

Under general boundary conditions we consider the finiteness of the Hausdorff and fractal dimensions of the global attractor for the strong solution of the 3D moist primitive equations with viscosity. Firstly, we obtain time-uniform estimates of the first-order time derivative of the strong solutions in \begin{document}$L^2(\mho)$\end{document}. Then, to prove the finiteness of the Hausdorff and fractal dimensions of the global attractor, the common method is to obtain the uniform boundedness of the strong solution in \begin{document}$H^2(\mho)$\end{document} to establish the squeezing property of the solution operator. But it is difficult to achieve due to the boundary conditions and complicated structure of the 3D moist primitive equations. To overcome the difficulties, we try to use the uniform boundedness of the derivative of the strong solutions with respect to time \begin{document}$t$\end{document} in \begin{document}$L^2(\mho)$\end{document} to prove the uniform continuity of the global attractor. Finally, using the uniform continuity of the global attractor we establish the squeezing property of the solution operator which implies the finiteness of the Hausdorff and fractal dimensions of the global attractor.

Stabilization of turning processes using spindle feedback with state-dependent delay
Qingwen Hu and Huan Zhang
2018, 23(10) : 4329-4360 doi: 10.3934/dcdsb.2018167 +[Abstract](340) +[HTML](203) +[PDF](374.58KB)

We develop a stabilization strategy of turning processes by means of delayed spindle control. We show that turning processes which contain intrinsic state-dependent delays can be stabilized by a spindle control with state-dependent delay, and develop analytical description of the stability region in the parameter space. Numerical simulations stability region are also given to illustrate the general results.

Well-posedeness and energy decay of solutions to a bresse system with a boundary dissipation of fractional derivative type
Abbes Benaissa and Abderrahmane Kasmi
2018, 23(10) : 4361-4395 doi: 10.3934/dcdsb.2018168 +[Abstract](395) +[HTML](230) +[PDF](532.0KB)

We consider the Bresse system with three control boundary conditions of fractional derivative type. We prove the polynomial decay result with an estimation of the decay rates. Our result is established using the semigroup theory of linear operators and a result obtained by Borichev and Tomilov.

Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model
Jan Giesselmann, Niklas Kolbe, Mária Lukáčová-Medvi${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over d} }}$ová and Nikolaos Sfakianakis
2018, 23(10) : 4397-4431 doi: 10.3934/dcdsb.2018169 +[Abstract](354) +[HTML](219) +[PDF](988.3KB)

We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix.

We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

A vicinal surface model for epitaxial growth with logarithmic free energy
Yuan Gao, Hangjie Ji, Jian-Guo Liu and Thomas P. Witelski
2018, 23(10) : 4433-4453 doi: 10.3934/dcdsb.2018170 +[Abstract](305) +[HTML](222) +[PDF](1168.3KB)

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, \begin{document}$u_t = -u^2(u^3+α u)_{hhhh}$\end{document}, gives the evolution for the surface slope \begin{document}$u$\end{document} as a function of the local height \begin{document}$h$\end{document} in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of \begin{document}$u$\end{document} converging to a constant that only depends on the initial data is also investigated both analytically and numerically.

Convergence rate of strong approximations of compound random maps, application to SPDEs
Emmanuel Gobet and Mohamed Mrad
2018, 23(10) : 4455-4476 doi: 10.3934/dcdsb.2018171 +[Abstract](291) +[HTML](250) +[PDF](639.96KB)

We consider a random map \begin{document}$x\mapsto F(ω,x)$\end{document} and a random variable \begin{document}$Θ(ω)$\end{document}, and we denote by \begin{document}${{F}^{N}}(ω,x) $\end{document} and \begin{document}$ {{\Theta }^{N}}(ω) $\end{document} their approximations: We establish a strong convergence result, in \begin{document}${\bf{L}}_p$\end{document}-norms, of the compound approximation \begin{document}${{F}^{N}}(ω,{{\Theta }^{N}}(ω) )$\end{document} to the compound variable \begin{document}$F(ω,Θ(ω)) $\end{document}, in terms of the approximations of \begin{document}$F$\end{document} and \begin{document}$Θ$\end{document}. We then apply this result to the composition of two Stochastic Differential Equations (SDEs) through their initial conditions, which can give a way to solve some Stochastic Partial Differential Equations (SPDEs), in particular those from stochastic utilities.

Convergence of solutions to inverse problems for a class of variational-hemivariational inequalities
Stanisław Migórski and Biao Zeng
2018, 23(10) : 4477-4498 doi: 10.3934/dcdsb.2018172 +[Abstract](377) +[HTML](205) +[PDF](475.26KB)

The paper investigates an inverse problem for a stationary variational-hemivariational inequality. The solution of the variational-hemivariational inequality is approximated by its penalized version. We prove existence of solutions to inverse problems for both the initial inequality problem and the penalized problem. We show that optimal solutions to the inverse problem for the penalized problem converge, up to a subsequence, when the penalty parameter tends to zero, to an optimal solution of the inverse problem for the initial variational-hemivariational inequality. The results are illustrated by a mathematical model of a nonsmooth contact problem from elasticity.

Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment
Chengxia Lei, Fujun Li and Jiang Liu
2018, 23(10) : 4499-4517 doi: 10.3934/dcdsb.2018173 +[Abstract](353) +[HTML](267) +[PDF](455.28KB)

In this paper, we deal with a diffusive SIR epidemic model with nonlinear incidence of the form \begin{document}$I^pS^q$\end{document} for \begin{document}$0<p≤1$\end{document} in a heterogeneous environment. We establish the boundedness and uniform persistence of solutions to the system, and the global stability of the constant endemic equilibrium in the case of homogeneous environment. When the spatial environment is heterogeneous, we determine the asymptotic profile of endemic equilibrium if the diffusion rate of the susceptible or infected population is small. Our theoretical analysis shows that, different from the studies of [1,28,38,44] for the SIS models, restricting the movement of the susceptible or infected population can not lead to the extinction of infectious disease for such an SIR system.

Numerical study of phase transition in van der Waals fluid
Qiaolin He, Chang Liu and Xiaoding Shi
2018, 23(10) : 4519-4540 doi: 10.3934/dcdsb.2018174 +[Abstract](320) +[HTML](235) +[PDF](9009.6KB)

In this article, we use a relaxation scheme for conservation laws to study liquid-vapor phase transition modeled by the van der Waals equation, which introduces a small parameter $ε$ and a new variable. We solve the relaxation system in Lagrangian coordinates for one dimension and solve the system in Eulerian coordinates for two dimension. A second order TVD Runge-Kutta splitting scheme is used in time discretization and upwind or MUSCL scheme is used in space discretization. The long time behavior of the fluid is numerically investigated. If the initial data belongs to elliptic region, the solution converges to two Maxwell states. When the initial data lies in metastable region, the solution either remains in the same phase or converges to the Maxwell states depending to the initial perturbation. If the initial state is in the stable region, the solution remains in that region for all time.

Identification of generic stable dynamical systems taking a nonlinear differential approach
Mahdi Khajeh Salehani
2018, 23(10) : 4541-4555 doi: 10.3934/dcdsb.2018175 +[Abstract](520) +[HTML](295) +[PDF](467.84KB)

Identifying new stable dynamical systems, such as generic stable mechanical or electrical control systems, requires questing for the desired systems parameters that introduce such systems. In this paper, a systematic approach to construct generic stable dynamical systems is proposed. In fact, our approach is based on a simple identification method in which we intervene directly with the dynamics of our system by considering a continuous \begin{document}$1$\end{document}-parameter family of system parameters, being parametrized by a positive real variable \begin{document}$\ell$\end{document}, and then identify the desired parameters that introduce a generic stable dynamical system by analyzing the solutions of a special system of nonlinear functional-differential equations associated with the \begin{document}$\ell$\end{document}-varying parameters. We have also investigated the reliability and capability of our proposed approach.

To illustrate the utility of our result and as some applications of the nonlinear differential approach proposed in this paper, we conclude with considering a class of coupled spring-mass-dashpot systems, as well as the compartmental systems - the latter of which provide a mathematical model for many complex biological and physical processes having several distinct but interacting phases.

A reaction-diffusion-advection SIS epidemic model in a spatially-temporally heterogeneous environment
Danhua Jiang, Zhi-Cheng Wang and Liang Zhang
2018, 23(10) : 4557-4578 doi: 10.3934/dcdsb.2018176 +[Abstract](445) +[HTML](207) +[PDF](477.44KB)

In this paper, we study the effects of diffusion and advection for an SIS epidemic reaction-diffusion-advection model in a spatially and temporally heterogeneous environment. We introduce the basic reproduction number \begin{document} $\mathcal{R}_{0}$ \end{document} and establish the threshold-type results on the global dynamics in terms of \begin{document} $\mathcal{R}_{0}$ \end{document}. Some general qualitative properties of \begin{document} $\mathcal{R}_{0}$ \end{document} are presented, then the paper is devoted to studying how the advection and diffusion of the infected individuals affect the reproduction number \begin{document} $\mathcal{R}_{0}$ \end{document} for the special case that \begin{document} $γ(x,t)-β(x,t) = V(x,t)$ \end{document} is monotone with respect to spatial variable \begin{document} $x$ \end{document}. Our results suggest that if \begin{document} $V_{x}(x,t)≥0,\not\equiv0$ \end{document} and \begin{document} $V(x, t)$ \end{document} changes sign about \begin{document} $x$ \end{document}, the advection is beneficial to eliminate the disease, whereas if \begin{document} $V_{x}(x,t)≤0,\not\equiv0$ \end{document} and \begin{document} $V(x, t)$ \end{document} changes sign about \begin{document} $x$ \end{document}, the advection is bad for the elimination of disease.

Prevalence of stable periodic solutions in the forced relativistic pendulum equation
Feng Wang, Jifeng Chu and Zaitao Liang
2018, 23(10) : 4579-4594 doi: 10.3934/dcdsb.2018177 +[Abstract](359) +[HTML](211) +[PDF](400.41KB)

We study the prevalence of stable periodic solutions of the forced relativistic pendulum equation for external force which guarantees the existence of periodic solutions. We prove the results for a general planar system.

Time-dependent asymptotic behavior of the solution for plate equations with linear memory
Tingting Liu and Qiaozhen Ma
2018, 23(10) : 4595-4616 doi: 10.3934/dcdsb.2018178 +[Abstract](398) +[HTML](224) +[PDF](509.83KB)

In this article, we consider the long-time behavior of solutions for the plate equation with linear memory. Within the theory of process on time-dependent spaces, we investigate the existence of the time-dependent attractor by using the operator decomposition technique and compactness of translation theorem and more detailed estimates. Furthermore, the asymptotic structure of time-dependent attractor, which converges to the attractor of fourth order parabolic equation with memory, is proved. Besides, we obtain a further regular result.

Predicting and estimating probability density functions of chaotic systems
Noah H. Rhee, Paweł Góra and Majid Bani-Yaghoub
2017doi: 10.3934/dcdsb.2017144 +[Abstract](1228) +[HTML](695) +[PDF](463.5KB)
Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains
Xinguang Yang, Baowei Feng, Thales Maier de Souza and Taige Wang
2018doi: 10.3934/dcdsb.2018084 +[Abstract](565) +[HTML](402) +[PDF](467.51KB)
A locking free Reissner-Mindlin element with weak Galerkin rotations
Ruishu Wang, Lin Mu and Xiu Ye
2018doi: 10.3934/dcdsb.2018086 +[Abstract](577) +[HTML](396) +[PDF](367.32KB)
A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations
Wenbin Chen, Wenqiang Feng, Yuan Liu, Cheng Wang and Steven M. Wise
2018doi: 10.3934/dcdsb.2018090 +[Abstract](672) +[HTML](411) +[PDF](4796.31KB)
Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes
Qilong Zhai and Ran Zhang
2018doi: 10.3934/dcdsb.2018091 +[Abstract](571) +[HTML](399) +[PDF](351.95KB)
Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces
Chao Deng and Tong Li
2018doi: 10.3934/dcdsb.2018093 +[Abstract](578) +[HTML](388) +[PDF](408.35KB)
A period doubling route to spatiotemporal chaos in a system of Ginzburg-Landau equations for nematic electroconvection
Iuliana Oprea and Gerhard Dangelmayr
2018doi: 10.3934/dcdsb.2018095 +[Abstract](574) +[HTML](407) +[PDF](8917.37KB)
Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation
Aslihan Demirkaya and Milena Stanislavova
2018doi: 10.3934/dcdsb.2018097 +[Abstract](585) +[HTML](410) +[PDF](2559.58KB)
Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics
Naveen K. Vaidya, Xianping Li and Feng-Bin Wang
2018doi: 10.3934/dcdsb.2018099 +[Abstract](631) +[HTML](457) +[PDF](992.67KB)
A Comparison of some numerical conformal mapping methods for simply and multiply connected domains
Mohamed Badreddine, Thomas K. DeLillo and Saman Sahraei
2018doi: 10.3934/dcdsb.2018100 +[Abstract](608) +[HTML](531) +[PDF](2817.98KB)
Global regularity results for the climate model with fractional dissipation
Boqing Dong, Wenjuan Wang, Jiahong Wu and Hui Zhang
2018doi: 10.3934/dcdsb.2018102 +[Abstract](505) +[HTML](366) +[PDF](447.41KB)
Superconvergence of the semi-discrete local discontinuous Galerkin method for nonlinear KdV-type problems
Mahboub Baccouch
2018doi: 10.3934/dcdsb.2018104 +[Abstract](702) +[HTML](411) +[PDF](16469.35KB)
An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model
Mahadevan Ganesh, Brandon C. Reyes and Avi Purkayastha
2018doi: 10.3934/dcdsb.2018107 +[Abstract](556) +[HTML](462) +[PDF](727.13KB)
Two-grid finite element method for the stabilization of mixed Stokes-Darcy model
Jiaping Yu, Haibiao Zheng, Feng Shi and Ren Zhao
2018doi: 10.3934/dcdsb.2018109 +[Abstract](914) +[HTML](476) +[PDF](4434.43KB)
A comparative study on nonlocal diffusion operators related to the fractional Laplacian
Siwei Duo, Hong Wang and Yanzhi Zhang
2018doi: 10.3934/dcdsb.2018110 +[Abstract](669) +[HTML](669) +[PDF](1838.96KB)
A dimension splitting and characteristic projection method for three-dimensional incompressible flow
Hao Chen, Kaitai Li, Yuchuan Chu, Zhiqiang Chen and Yiren Yang
2018doi: 10.3934/dcdsb.2018111 +[Abstract](632) +[HTML](425) +[PDF](4837.74KB)
Modulus metrics on networks
Nathan Albin, Nethali Fernando and Pietro Poggi-Corradini
2018doi: 10.3934/dcdsb.2018161 +[Abstract](279) +[HTML](190) +[PDF](564.28KB)
Balanced truncation model reduction of a nonlinear cable-mass PDE system with interior damping
Belinda A. Batten, Hesam Shoori, John R. Singler and Madhuka H. Weerasinghe
2018doi: 10.3934/dcdsb.2018162 +[Abstract](311) +[HTML](201) +[PDF](994.3KB)
Existence and uniqueness of solutions of free boundary problems in heterogeneous environments
Mingxin Wang
2018doi: 10.3934/dcdsb.2018179 +[Abstract](412) +[HTML](210) +[PDF](302.43KB)
Global existence for an attraction-repulsion chemotaxis fluid model with logistic source
Abelardo Duarte-Rodríguez, Lucas C. F. Ferreira and Élder J. Villamizar-Roa
2018doi: 10.3934/dcdsb.2018180 +[Abstract](353) +[HTML](221) +[PDF](564.89KB)
Asymptotic behavior of stochastic complex Ginzburg-Landau equations with deterministic non-autonomous forcing on thin domains
Dingshi Li and Xiaohu Wang
2018doi: 10.3934/dcdsb.2018181 +[Abstract](334) +[HTML](198) +[PDF](412.42KB)
Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity
Qingyan Shi, Junping Shi and Yongli Song
2018doi: 10.3934/dcdsb.2018182 +[Abstract](461) +[HTML](218) +[PDF](1057.62KB)
Spatiotemporal attractors generated by the Turing-Hopf bifurcation in a time-delayed reaction-diffusion system
Qi An and Weihua Jiang
2018doi: 10.3934/dcdsb.2018183 +[Abstract](353) +[HTML](282) +[PDF](2451.29KB)
Bistable waves of a recursive system arising from seasonal age-structured population models
Yingli Pan, Ying Su and Junjie Wei
2018doi: 10.3934/dcdsb.2018184 +[Abstract](311) +[HTML](207) +[PDF](422.62KB)
The regularity of pullback attractor for a non-autonomous p-Laplacian equation with dynamical boundary condition
Wen Tan
2018doi: 10.3934/dcdsb.2018194 +[Abstract](370) +[HTML](224) +[PDF](451.81KB)
Cosymmetry approach and mathematical modeling of species coexistence in a heterogeneous habitat
Alexander V. Budyansky, Kurt Frischmuth and Vyacheslav G. Tsybulin
2018doi: 10.3934/dcdsb.2018196 +[Abstract](366) +[HTML](140) +[PDF](757.88KB)
Efficient representation of invariant manifolds of periodic orbits in the CRTBP
Roberto Castelli
2018doi: 10.3934/dcdsb.2018197 +[Abstract](342) +[HTML](237) +[PDF](10671.43KB)
Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation
Wei Mao, Liangjian Hu and Xuerong Mao
2018doi: 10.3934/dcdsb.2018198 +[Abstract](361) +[HTML](169) +[PDF](460.52KB)
Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion
Litan Yan and Xiuwei Yin
2018doi: 10.3934/dcdsb.2018199 +[Abstract](294) +[HTML](165) +[PDF](436.11KB)
Advection-diffusion equation on a half-line with boundary Lévy noise
Lena-Susanne Hartmann and Ilya Pavlyukevich
2018doi: 10.3934/dcdsb.2018200 +[Abstract](318) +[HTML](165) +[PDF](517.31KB)
Persistent two-dimensional strange attractors for a two-parameter family of Expanding Baker Maps
Antonio Pumariño, José Ángel Rodríguez and Enrique Vigil
2018doi: 10.3934/dcdsb.2018201 +[Abstract](255) +[HTML](155) +[PDF](401.71KB)
Invasion fronts on graphs: The Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphs
Aaron Hoffman and Matt Holzer
2018doi: 10.3934/dcdsb.2018202 +[Abstract](247) +[HTML](156) +[PDF](973.77KB)
Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments
Yulan Lu, Minghui Song and Mingzhu Liu
2018doi: 10.3934/dcdsb.2018203 +[Abstract](325) +[HTML](159) +[PDF](550.13KB)
The Rothe method for multi-term time fractional integral diffusion equations
Stanisław Migórski and Shengda Zeng
2018doi: 10.3934/dcdsb.2018204 +[Abstract](264) +[HTML](218) +[PDF](379.33KB)
Dirac-concentrations in an integro-pde model from evolutionary game theory
King-Yeung Lam
2018doi: 10.3934/dcdsb.2018205 +[Abstract](244) +[HTML](147) +[PDF](589.14KB)
Valuation of American strangle option: Variational inequality approach
Junkee Jeon and Jehan Oh
2018doi: 10.3934/dcdsb.2018206 +[Abstract](315) +[HTML](158) +[PDF](548.5KB)
Global dynamics of a latent HIV infection model with general incidence function and multiple delays
Yu Yang, Yueping Dong and Yasuhiro Takeuchi
2018doi: 10.3934/dcdsb.2018207 +[Abstract](436) +[HTML](169) +[PDF](1116.75KB)
A two-species weak competition system of reaction-diffusion-advection with double free boundaries
Bo Duan and Zhengce Zhang
2018doi: 10.3934/dcdsb.2018208 +[Abstract](264) +[HTML](185) +[PDF](517.73KB)
Boundedness in a three-dimensional Keller-Segel- Stokes system involving tensor-valued sensitivity with saturation
Dan Li, Chunlai Mu, Pan Zheng and Ke Lin
2018doi: 10.3934/dcdsb.2018209 +[Abstract](277) +[HTML](145) +[PDF](520.67KB)
Mean field model for collective motion bistability
Josselin Garnier, George Papanicolaou and Tzu-Wei Yang
2018doi: 10.3934/dcdsb.2018210 +[Abstract](252) +[HTML](140) +[PDF](5851.55KB)
Limit cycles for regularized piecewise smooth systems with a switching manifold of codimension two
Dingheng Pi
2018doi: 10.3934/dcdsb.2018211 +[Abstract](329) +[HTML](147) +[PDF](357.85KB)
Global weak solutions for a coupled chemotaxis non-Newtonian fluid
Hafedh Bousbih
2018doi: 10.3934/dcdsb.2018212 +[Abstract](332) +[HTML](189) +[PDF](515.27KB)
Traveling wave solutions for a bacteria system with density-suppressed motility
Roger Lui and Hirokazu Ninomiya
2018doi: 10.3934/dcdsb.2018213 +[Abstract](517) +[HTML](251) +[PDF](216.77KB)
Thermodynamical potentials of classical and quantum systems
Ruikuan Liu, Tian Ma, Shouhong Wang and Jiayan Yang
2018doi: 10.3934/dcdsb.2018214 +[Abstract](230) +[HTML](122) +[PDF](637.0KB)
On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
Huijie Qiao and Jiang-Lun Wu
2018doi: 10.3934/dcdsb.2018215 +[Abstract](228) +[HTML](135) +[PDF](423.33KB)
Dynamic behavior and optimal scheduling for mixed vaccination strategy with temporary immunity
Siyu Liu, Xue Yang, Yingjie Bi and Yong Li
2018doi: 10.3934/dcdsb.2018216 +[Abstract](304) +[HTML](138) +[PDF](653.24KB)
Non-autonomous reaction-diffusion equations with variable exponents and large diffusion
Antonio Carlos Fernandes, Marcela Carvalho Gonçcalves and Jacson Simsen
2018doi: 10.3934/dcdsb.2018217 +[Abstract](280) +[HTML](139) +[PDF](3152.45KB)
Uniqueness and stability of traveling waves for a three-species competition system with nonlocal dispersal
Guo-Bao Zhang, Fang-Di Dong and Wan-Tong Li
2018doi: 10.3934/dcdsb.2018218 +[Abstract](325) +[HTML](156) +[PDF](472.18KB)
Fluctuations of mRNA distributions in multiple pathway activated transcription
Genghong Lin, Jianshe Yu, Zhan Zhou, Qiwen Sun and Feng Jiao
2018doi: 10.3934/dcdsb.2018219 +[Abstract](265) +[HTML](263) +[PDF](722.11KB)
Global existence and stability in a two-species chemotaxis system
Huanhuan Qiu and Shangjiang Guo
2018doi: 10.3934/dcdsb.2018220 +[Abstract](261) +[HTML](287) +[PDF](1061.01KB)
Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space
Suna Ma, Huiyuan Li and Zhimin Zhang
2018doi: 10.3934/dcdsb.2018221 +[Abstract](254) +[HTML](193) +[PDF](7354.7KB)
Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems
Liang Ding, Rongrong Tian and Jinlong Wei
2018doi: 10.3934/dcdsb.2018222 +[Abstract](309) +[HTML](144) +[PDF](325.95KB)
A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients
Yizhuo Wang and Shangjiang Guo
2018doi: 10.3934/dcdsb.2018223 +[Abstract](264) +[HTML](236) +[PDF](483.02KB)
Synchronization of first-order autonomous oscillators on Riemannian manifolds
Simone Fiori
2018doi: 10.3934/dcdsb.2018233 +[Abstract](139) +[HTML](76) +[PDF](2697.39KB)
Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time
Vladimir Gaitsgory, Alex Parkinson and Ilya Shvartsman
2018doi: 10.3934/dcdsb.2018235 +[Abstract](128) +[HTML](80) +[PDF](512.69KB)
Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center
Jaume Llibre and Yilei Tang
2018doi: 10.3934/dcdsb.2018236 +[Abstract](151) +[HTML](95) +[PDF](418.99KB)
Spatial propagation for a parabolic system with multiple species competing for single resource
Zhiguo Wang, Hua Nie and Jianhua Wu
2018doi: 10.3934/dcdsb.2018237 +[Abstract](115) +[HTML](123) +[PDF](537.12KB)
Swarming in domains with boundaries: Approximation and regularization by nonlinear diffusion
Razvan C. Fetecau, Mitchell Kovacic and Ihsan Topaloglu
2018doi: 10.3934/dcdsb.2018238 +[Abstract](146) +[HTML](62) +[PDF](1343.26KB)
Spreading-vanishing dichotomy in information diffusion in online social networks with intervention
Jingli Ren, Dandan Zhu and Haiyan Wang
2018doi: 10.3934/dcdsb.2018240 +[Abstract](180) +[HTML](80) +[PDF](3790.08KB)
Periodic attractors of nonautonomous flat-topped tent systems
Luís Silva
2018doi: 10.3934/dcdsb.2018243 +[Abstract](128) +[HTML](74) +[PDF](315.98KB)
Evolutionarily stable dispersal strategies in a two-patch advective environment
Jing-Jing Xiang and Yihao Fang
2018doi: 10.3934/dcdsb.2018245 +[Abstract](113) +[HTML](73) +[PDF](444.2KB)
Asymptotic behavior for stochastic plate equations with rotational inertia and Kelvin-Voigt dissipative term on unbounded domains
Xiaobin Yao, Qiaozhen Ma and Tingting Liu
2018doi: 10.3934/dcdsb.2018247 +[Abstract](186) +[HTML](77) +[PDF](501.98KB)
Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics
Hai-Yang Jin and Tian Xiang
2018doi: 10.3934/dcdsb.2018249 +[Abstract](129) +[HTML](66) +[PDF](526.21KB)
Smoothing dynamics of the non-autonomous stochastic Fitzhugh-Nagumo system on $\mathbb{R}^N$ driven by multiplicative noises
Wenqiang Zhao
2018doi: 10.3934/dcdsb.2018251 +[Abstract](143) +[HTML](84) +[PDF](461.94KB)
A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
Raphael Kruse and Yue Wu
2018doi: 10.3934/dcdsb.2018253 +[Abstract](161) +[HTML](107) +[PDF](608.47KB)
Numerical methods for PDE models related to pricing and expected lifetime of an extraction project under uncertainty
María Suárez-Taboada and Carlos Vázquez
2018doi: 10.3934/dcdsb.2018254 +[Abstract](171) +[HTML](83) +[PDF](650.04KB)
Hermite spectral method for Long-Short wave equations
Shujuan Lü, Zeting Liu and Zhaosheng Feng
2018doi: 10.3934/dcdsb.2018255 +[Abstract](9) +[HTML](9) +[PDF](440.98KB)
Lyapunov type inequalities for Hammerstein integral equations and applications to population dynamics
Kunquan Lan and Wei Lin
2018doi: 10.3934/dcdsb.2018256 +[Abstract](17) +[HTML](8) +[PDF](502.25KB)
Global exponential attraction for multi-valued semidynamical systems with application to delay differential equations without uniqueness
Yejuan Wang and Lin Yang
2018doi: 10.3934/dcdsb.2018257 +[Abstract](13) +[HTML](10) +[PDF](490.61KB)
Confinement of a hot temperature patch in the modified SQG model
Roberto Garra
2018doi: 10.3934/dcdsb.2018258 +[Abstract](15) +[HTML](11) +[PDF](320.99KB)
Oscillations and asymptotic convergence for a delay differential equation modeling platelet production
Loïs Boullu, Mostafa Adimy, Fabien Crauste and Laurent Pujo-Menjouet
2018doi: 10.3934/dcdsb.2018259 +[Abstract](19) +[HTML](8) +[PDF](591.42KB)
Asymptotics of the Lebowitz-Rubinow-Rotenberg model of population development
Adam Gregosiewicz
2018doi: 10.3934/dcdsb.2018260 +[Abstract](13) +[HTML](8) +[PDF](641.03KB)
Symmetries of nonlinear vibrations in tetrahedral molecular configurations
Irina Berezovik, Carlos García-Azpeitia and Wieslaw Krawcewicz
2018doi: 10.3934/dcdsb.2018261 +[Abstract](24) +[HTML](11) +[PDF](274.11KB)
Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations
Peng Gao
2018doi: 10.3934/dcdsb.2018262 +[Abstract](13) +[HTML](8) +[PDF](354.81KB)
Global Eradication for Spatially Structured Populations by Regional Control
Sebastian Aniţa, Vincenzo Capasso and Ana-Maria Moşneagu
2018doi: 10.3934/dcdsb.2018263 +[Abstract](14) +[HTML](9) +[PDF](466.08KB)
Stability and bifurcation in an age-structured model with stocking rate and time delays
Shengqin Xu, Chuncheng Wang and Dejun Fan
2018doi: 10.3934/dcdsb.2018264 +[Abstract](13) +[HTML](8) +[PDF](471.73KB)
On the long-time behaviour of age and trait structured population dynamics
Tristan Roget
2018doi: 10.3934/dcdsb.2018265 +[Abstract](18) +[HTML](8) +[PDF](578.84KB)
Optimal control problems for the Gompertz model under the Norton-Simon hypothesis in chemotherapy
Luis A. Fernández and Cecilia Pola
2018doi: 10.3934/dcdsb.2018266 +[Abstract](12) +[HTML](7) +[PDF](616.77KB)
Global solution and decay rate for a reduced gravity two and a half layer model
Yongming Liu and Lei Yao
2018doi: 10.3934/dcdsb.2018267 +[Abstract](11) +[HTML](9) +[PDF](262.77KB)
Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study
Tomás Caraballo, Renato Colucci and Luca Guerrini
2018doi: 10.3934/dcdsb.2018268 +[Abstract](16) +[HTML](9) +[PDF](1025.84KB)
Stability of radial solutions of the Poisson-Nernst-Planck system in annular domains
Chia-Yu Hsieh
2018doi: 10.3934/dcdsb.2018269 +[Abstract](11) +[HTML](6) +[PDF](450.71KB)
Nondegenerate multistationarity in small reaction networks
Anne Shiu and Timo de Wolff
2018doi: 10.3934/dcdsb.2018270 +[Abstract](10) +[HTML](11) +[PDF](413.58KB)
Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
Ruyun Ma and Man Xu
2018doi: 10.3934/dcdsb.2018271 +[Abstract](17) +[HTML](10) +[PDF](444.31KB)
Long time behavior of fractional impulsive stochastic differential equations with infinite delay
Jiaohui Xu and Tomás Caraballo
2018doi: 10.3934/dcdsb.2018272 +[Abstract](26) +[HTML](12) +[PDF](547.29KB)
H2-stability of some second order fully discrete schemes for the Navier-Stokes equations
Yinnian He, Pengzhan Huang and Jian Li
2018doi: 10.3934/dcdsb.2018273 +[Abstract](15) +[HTML](7) +[PDF](398.58KB)
Immunosuppressant treatment dynamics in renal transplant recipients: an iterative modeling approach
Neha Murad, H. T. Tran, H. T. Banks, R. A. Everett and Eric S. Rosenberg
2018doi: 10.3934/dcdsb.2018274 +[Abstract](13) +[HTML](10) +[PDF](2017.44KB)
Distribution profiles in gene transcription activated by the cross-talking pathway
Feng Jiao, Qiwen Sun, Genghong Lin and Jianshe Yu
2018doi: 10.3934/dcdsb.2018275 +[Abstract](10) +[HTML](6) +[PDF](764.57KB)
Convergences of asymptotically autonomous pullback attractors towards semigroup attractors
Hongyong Cui
2018doi: 10.3934/dcdsb.2018276 +[Abstract](17) +[HTML](9) +[PDF](475.92KB)
Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems
Victor Kozyakin
2018doi: 10.3934/dcdsb.2018277 +[Abstract](23) +[HTML](10) +[PDF](532.88KB)
On asymptotically autonomous dynamics for multivalued evolution problems
Jacson Simsen and Mariza Stefanello Simsen
2018doi: 10.3934/dcdsb.2018278 +[Abstract](9) +[HTML](11) +[PDF](330.5KB)
Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping
Daniel Pardo, José Valero and Ángel Giménez
2018doi: 10.3934/dcdsb.2018279 +[Abstract](18) +[HTML](7) +[PDF](4075.25KB)
Modeling and analysis of random and stochastic input flows in the chemostat model
Tomás Caraballo, Maria-José Garrido-Atienza, Javier López-de-la-Cruz and Alain Rapaport
2018doi: 10.3934/dcdsb.2018280 +[Abstract](10) +[HTML](10) +[PDF](572.67KB)
On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass
Ghada Ben Belgacem and Chaker Jammazi
2018doi: 10.3934/dcdsb.2018286 +[Abstract](133) +[HTML](96) +[PDF](491.06KB)
Hierarchies and Hamiltonian structures of the Nonlinear Schrödinger family using geometric and spectral techniques
Partha Guha and Indranil Mukherjee
2018doi: 10.3934/dcdsb.2018287 +[Abstract](126) +[HTML](74) +[PDF](391.27KB)
Convex geometry of the carrying simplex for the May-Leonard map
Stephen Baigent
2018doi: 10.3934/dcdsb.2018288 +[Abstract](114) +[HTML](84) +[PDF](925.86KB)
Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation
Jean-Frédéric Gerbeau and Benoit Perthame
2001, 1(1) : 89-102 doi: 10.3934/dcdsb.2001.1.89 +[Abstract](1556) +[PDF](239.9KB) Cited By(102)
Optimal control of treatments in a two-strain tuberculosis model
E. Jung, Suzanne Lenhart and Z. Feng
2002, 2(4) : 473-482 doi: 10.3934/dcdsb.2002.2.473 +[Abstract](1300) +[PDF](139.6KB) Cited By(92)
Analysis of upscaling absolute permeability
X.H. Wu, Y. Efendiev and Thomas Y. Hou
2002, 2(2) : 185-204 doi: 10.3934/dcdsb.2002.2.185 +[Abstract](891) +[PDF](226.2KB) Cited By(71)
Fisher waves in an epidemic model
Xiao-Qiang Zhao and Wendi Wang
2004, 4(4) : 1117-1128 doi: 10.3934/dcdsb.2004.4.1117 +[Abstract](980) +[PDF](197.7KB) Cited By(62)
Optimal control of vector-borne diseases: Treatment and prevention
Kbenesh Blayneh, Yanzhao Cao and Hee-Dae Kwon
2009, 11(3) : 587-611 doi: 10.3934/dcdsb.2009.11.587 +[Abstract](1354) +[PDF](596.7KB) Cited By(59)
Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay
Huiyan Zhu and Xingfu Zou
2009, 12(2) : 511-524 doi: 10.3934/dcdsb.2009.12.511 +[Abstract](1005) +[PDF](264.3KB) Cited By(59)
Modelling and analysis of integrated pest management strategy
Sanyi Tang and Lansun Chen
2004, 4(3) : 759-768 doi: 10.3934/dcdsb.2004.4.759 +[Abstract](1251) +[PDF](161.3KB) Cited By(49)
Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian
Adam M. Oberman
2008, 10(1) : 221-238 doi: 10.3934/dcdsb.2008.10.221 +[Abstract](952) +[PDF](2040.6KB) Cited By(48)
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: Numerical algorithms
Àlex Haro and Rafael de la Llave
2006, 6(6) : 1261-1300 doi: 10.3934/dcdsb.2006.6.1261 +[Abstract](535) +[PDF](479.5KB) Cited By(46)
Infinite propagation speed for a two component Camassa-Holm equation
David Henry
2009, 12(3) : 597-606 doi: 10.3934/dcdsb.2009.12.597 +[Abstract](911) +[PDF](181.0KB) Cited By(46)
Positive solutions to the unstirred chemostat model with Crowley-Martin functional response
Hai-Xia Li, Jian-Hua Wu, Yan-Ling Li and Chun-An Liu
2018, 23(8) : 2951-2966 doi: 10.3934/dcdsb.2017128 +[Abstract](1551) +[HTML](644) +[PDF](481.89KB) PDF Downloads(290)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2018, 23(8) : 2967-2988 doi: 10.3934/dcdsb.2017149 +[Abstract](2309) +[HTML](1002) +[PDF](566.06KB) PDF Downloads(260)
A stochastic SIRI epidemic model with Lévy noise
Badr-eddine Berrhazi, Mohamed El Fatini, Tomás Caraballo and Roger Pettersson
2018, 23(9) : 3645-3661 doi: 10.3934/dcdsb.2018057 +[Abstract](1344) +[HTML](655) +[PDF](2371.8KB) PDF Downloads(186)
Asymptotic behaviour of the solutions to a virus dynamics model with diffusion
Toru Sasaki and Takashi Suzuki
2018, 23(2) : 525-541 doi: 10.3934/dcdsb.2017206 +[Abstract](1227) +[HTML](358) +[PDF](690.66KB) PDF Downloads(159)
Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity
Zhenguo Bai and Tingting Zhao
2018, 23(10) : 4063-4085 doi: 10.3934/dcdsb.2018126 +[Abstract](644) +[HTML](433) +[PDF](519.85KB) PDF Downloads(155)
Dynamics of a diffusive prey-predator system with strong Allee effect growth rate and a protection zone for the prey
Na Min and Mingxin Wang
2018, 23(4) : 1721-1737 doi: 10.3934/dcdsb.2018073 +[Abstract](1154) +[HTML](500) +[PDF](391.76KB) PDF Downloads(154)
Analysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays
Shihe Xu, Meng Bai and Fangwei Zhang
2018, 23(9) : 3535-3551 doi: 10.3934/dcdsb.2017213 +[Abstract](61756) +[HTML](744) +[PDF](416.76KB) PDF Downloads(150)
Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay
Igor Chueshov, Peter E. Kloeden and Meihua Yang
2018, 23(3) : 991-1009 doi: 10.3934/dcdsb.2018139 +[Abstract](896) +[HTML](390) +[PDF](479.0KB) PDF Downloads(147)
Pullback attractors for a class of non-autonomous thermoelastic plate systems
Flank D. M. Bezerra, Vera L. Carbone, Marcelo J. D. Nascimento and Karina Schiabel
2018, 23(9) : 3553-3571 doi: 10.3934/dcdsb.2017214 +[Abstract](1088) +[HTML](602) +[PDF](461.59KB) PDF Downloads(144)
Positive steady states of a density-dependent predator-prey model with diffusion
Kaigang Huang, Yongli Cai, Feng Rao, Shengmao Fu and Weiming Wang
2018, 23(8) : 3087-3107 doi: 10.3934/dcdsb.2017209 +[Abstract](1207) +[HTML](612) +[PDF](602.62KB) PDF Downloads(140)

2017  Impact Factor: 0.972




Email Alert

[Back to Top]