ISSN:
 1531-3492

eISSN:
 1553-524X

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

Export/Reference:

On optimal controls in coefficients for ill-posed non-Linear elliptic Dirichlet boundary value problems
Olha P. Kupenko and Rosanna Manzo
2018, 23(4) : 1363-1393 doi: 10.3934/dcdsb.2018155 +[Abstract](63) +[HTML](29) +[PDF](599.55KB)
Abstract:

We consider an optimal control problem associated to Dirichlet boundary value problem for non-linear elliptic equation on a bounded domain \begin{document}$Ω$ \end{document}. We take the coefficient \begin{document}$u(x)∈ L^∞(Ω)\cap BV(Ω)$ \end{document} in the main part of the non-linear differential operator as a control and in the linear part of differential operator we consider coefficients to be unbounded skew-symmetric matrix \begin{document}$A_{skew}∈ L^q(Ω;\mathbb{S}^N_{skew})$ \end{document}. We show that, in spite of unboundedness of the non-linear differential operator, the considered Dirichlet problem admits at least one weak solution and the corresponding OCP is well-possed and solvable. At the same time, optimal solutions to such problem can inherit a singular character of the matrices \begin{document}$A^{skew}$ \end{document}. We indicate two types of optimal solutions to the above problem and show that one of them can be attained by optimal solutions of regularized problems for coercive elliptic equations with bounded coefficients, using the two-parametric regularization of the initial OCP.

Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model
Haibo Cui, Qunyi Bie and Zheng-An Yao
2018, 23(4) : 1395-1410 doi: 10.3934/dcdsb.2018156 +[Abstract](55) +[HTML](33) +[PDF](459.69KB)
Abstract:

This paper is dedicated to the study of the Cauchy problem for a compressible viscous liquid-gas two-phase flow model in \begin{document}$\mathbb{R}^N\,(N≥2)$ \end{document}. We concentrate on the critical Besov spaces based on the \begin{document}$L^p$ \end{document} setting. We improve the range of Lebesgue exponent \begin{document}$p$ \end{document}, for which the system is locally well-posed, compared to [22]. Applying Lagrangian coordinates is the key to our statements, as it enables us to obtain the result by means of Banach fixed point theorem.

Global analysis of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain
Guochun Wu and Yinghui Zhang
2018, 23(4) : 1411-1429 doi: 10.3934/dcdsb.2018157 +[Abstract](53) +[HTML](37) +[PDF](439.63KB)
Abstract:

In this paper, we investigate global existence and asymptotic behavior of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain with no-slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in \begin{document}$H^2(Ω)$ \end{document}. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.

A time-delay in the activator kinetics enhances the stability of a spike solution to the gierer-meinhardt model
Nabil T. Fadai, Michael J. Ward and Juncheng Wei
2018, 23(4) : 1431-1458 doi: 10.3934/dcdsb.2018158 +[Abstract](53) +[HTML](33) +[PDF](752.47KB)
Abstract:

We study the spectrum of a new class of nonlocal eigenvalue problems (NLEPs) that characterize the linear stability properties of localized spike solutions to the singularly perturbed two-component Gierer-Meinhardt (GM) reaction-diffusion (RD) system with a fixed time-delay \begin{document}$T$\end{document} in only the nonlinear autocatalytic activator kinetics. Our analysis of this model is motivated by the computational study of Seirin Lee et al. [Bull. Math. Bio., 72(8), (2010)] on the effect of gene expression time delays on spatial patterning for both the GM and some related RD models. For various limiting forms of the GM model, we show from a numerical study of the associated NLEP, together with an analytical scaling law analysis valid for large delay \begin{document}$T$\end{document}, that a time-delay in only the activator kinetics is stabilizing in the sense that there is a wider region of parameter space where the spike solution is linearly stable than when there is no time delay. This enhanced stability behavior with a delayed activator kinetics is in marked contrast to the de-stabilizing effect on spike solutions of having a time-delay in both the activator and inhibitor kinetics. Numerical results computed from the RD system with delayed activator kinetics are used to validate the theory for the 1-D case.

Convergence of a finite volume scheme for a stochastic conservation law involving a $Q$-brownian motion
Tadahisa Funaki, Yueyuan Gao and Danielle Hilhorst
2018, 23(4) : 1459-1502 doi: 10.3934/dcdsb.2018159 +[Abstract](50) +[HTML](36) +[PDF](665.68KB)
Abstract:

We study a time explicit finite volume method for a first order conservation law with a multiplicative source term involving a \begin{document}$Q$\end{document}-Wiener process. After having presented the definition of a measure-valued weak entropy solution of the stochastic conservation law, we apply a finite volume method together with Godunov scheme for the space discretization, and we denote by \begin{document}$\{u_{\mathcal{T}, k}\}$\end{document} its discrete solution. We present some a priori estimates including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities for the discrete solution. We show that the discrete solution \begin{document}$\{u_{\mathcal{T}, k}\}$\end{document} converges along a subsequence to a measure-valued entropy solution of the conservation law in the sense of Young measures as the maximum diameter of the volume elements and the time step tend to zero. Some numerical simulations are presented in the case of the stochastic Burgers equation. The empirical average turns out to be a regularization of the deterministic solution; moreover, the variance in the case of the \begin{document}$Q$\end{document}-Brownian motion converges to a constant while that in the Brownian motion case keeps increasing as time tends to infinity.

An N-barrier maximum principle for elliptic systems arising from the study of traveling waves in reaction-diffusion systems
Chiun-Chuan Chen and Li-Chang Hung
2018, 23(4) : 1503-1521 doi: 10.3934/dcdsb.2018054 +[Abstract](234) +[HTML](170) +[PDF](720.55KB)
Abstract:

By employing the N-barrier method developed in C.-C. Chen and L.-C. Hung, 2016 ([6]), we establish a new N-barrier maximum principle for diffusive Lotka-Volterra systems of two competing species. To this end, this gives rise to the N-barrier maximum principle for a second-order elliptic equation involving two distinct unknown functions and a quadratic nonlinearity. An immediate consequence of the N-barrier maximum principle is an a priori estimate for the total populations of the two species. As an application of this maximum principle, we show under certain conditions the existence and nonexistence of traveling waves solutions for systems of three competing species. In addition, new \begin{document}$(1, 0, 0)$\end{document}-\begin{document}$(u^{*}, v^{*}, 0)$\end{document} waves are given in terms of the tanh function, provided that the system's parameters satisfy certain conditions.

Time fractional and space nonlocal stochastic boussinesq equations driven by gaussian white noise
Tianlong Shen, Jianhua Huang and Caibin Zeng
2018, 23(4) : 1523-1533 doi: 10.3934/dcdsb.2018056 +[Abstract](221) +[HTML](169) +[PDF](397.0KB)
Abstract:

We present the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein-Ulenbeck equations, and establish the existence and uniqueness of mild solutions for time fractional and space nonlocal stochastic Boussinesq equations driven by Gaussian white noise.

Longtime robustness and semi-uniform compactness of a pullback attractor via nonautonomous PDE
Yangrong Li, Lianbing She and Jinyan Yin
2018, 23(4) : 1535-1557 doi: 10.3934/dcdsb.2018058 +[Abstract](247) +[HTML](179) +[PDF](489.11KB)
Abstract:

This paper is concerned with the robustness of a pullback attractor as the time tends to infinity. A pullback attractor is called forward (resp. backward) compact if the union over the future (resp. the past) is pre-compact. We prove that the forward (resp. backward) compactness is a necessary and sufficient condition such that a pullback attractor is upper semi-continuous to a compact set at positive (resp. negative) infinity, and also obtain the minimal limit-set. We further prove the lower semi-continuity of the pullback attractor and get the maximal limit-set at infinity. Some criteria for such robustness are established when the evolution process is forward or backward omega-limit compact. Those theoretical criteria are applied to prove semi-uniform compactness and robustness at infinity in pullback dynamics for a Ginzburg-Landau equation with variable coefficients and a forward or backward tempered nonlinearity.

Dynamics of a Lotka-Volterra competition-diffusion model with stage structure and spatial heterogeneity
Shuling Yan and Shangjiang Guo
2018, 23(4) : 1559-1579 doi: 10.3934/dcdsb.2018059 +[Abstract](269) +[HTML](175) +[PDF](587.67KB)
Abstract:

This paper is concerned with a Lotka-Volterra competition-diffusion model with stage structure and spatial heterogeneity. By analyzing the sign of the principal eigenvalue corresponding to each semi-trivial solution, we obtain the linear stability and global attractivity of the semi-trivial solution. In addition, an attracting region was obtained by means of the method of upper and lower solutions.

Two codimension-two bifurcations of a second-order difference equation from macroeconomics
Jiyu Zhong and Shengfu Deng
2018, 23(4) : 1581-1600 doi: 10.3934/dcdsb.2018062 +[Abstract](237) +[HTML](164) +[PDF](723.32KB)
Abstract:

In this paper we mainly investigate two codimension-two bifurcations of a second-order difference equation from macroeconomics. Applying the center manifold theorem and the normal form analysis, we firstly give the parameter conditions for the generalized flip bifurcation, and prove that the system does not produce a strong resonance. Then, we compute the normal forms to obtain the parameter conditions for the Neimark-Sacker bifurcation, from which we present the conditions for the Chenciner bifurcation. In order to verify the correctness of our results, we also numerically simulate a half stable invariant circle and two invariant circles, one stable and one unstable, arising from the Chenciner bifurcation.

Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations
Katherine A. Kime
2018, 23(4) : 1601-1621 doi: 10.3934/dcdsb.2018063 +[Abstract](231) +[HTML](205) +[PDF](432.54KB)
Abstract:

We consider discrete potentials as controls in systems of finite difference equations which are discretizations of a 1-D Schrödinger equation. We give examples of palindromic potentials which have corresponding steerable initial-terminal pairs which are not mirror-symmetric. For a set of palindromic potentials, we show that the corresponding steerable pairs that satisfy a localization property are mirror-symmetric. We express the initial and terminal states in these pairs explicitly as scalar multiples of vector-valued functions of a parameter in the control.

Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: Analysis without electroneutrality boundary conditions
Hong Lu, Ji Li, Joseph Shackelford, Jeremy Vorenberg and Mingji Zhang
2018, 23(4) : 1623-1643 doi: 10.3934/dcdsb.2018064 +[Abstract](223) +[HTML](166) +[PDF](709.89KB)
Abstract:

A quasi-one-dimensional steady-state Poisson-Nernst-Planck model with Bikerman's local hard-sphere potential for ionic flows of two oppositely charged ion species through a membrane channel is analyzed. Of particular interest is the qualitative properties of ionic flows in terms of individual fluxes without the assumption of electroneutrality conditions, which is more realistic to study ionic flow properties of interest. This is the novelty of this work. Our result shows that ⅰ) boundary concentrations and relative size of ion species play critical roles in characterizing ion size effects on individual fluxes; ⅱ) the first order approximation \begin{document} $\mathcal{J}_{k1} = D_kJ_{k1}$ \end{document} in ion volume of individual fluxes \begin{document} $\mathcal{ J}_k = D_kJ_k$ \end{document} is linear in boundary potential, furthermore, the signs of \begin{document} $\partial_V \mathcal{ J}_{k1}$ \end{document} and \begin{document} $\partial^2_{Vλ} \mathcal{J}_{k1}$ \end{document}, which play key roles in characterizing ion size effects on ionic flows can be both negative depending further on boundary concentrations while they are always positive and independent of boundary concentrations under electroneutrality conditions (see Corollaries 3.2-3.3, Theorems 3.4-3.5 and Proposition 3.7). Numerical simulations are performed to identify some critical potentials defined in (2). We believe our results will provide useful insights for numerical and even experimental studies of ionic flows through membrane channels.

Dynamics for the damped wave equations on time-dependent domains
Feng Zhou, Chunyou Sun and Xin Li
2018, 23(4) : 1645-1674 doi: 10.3934/dcdsb.2018068 +[Abstract](448) +[HTML](277) +[PDF](619.97KB)
Abstract:

We consider the asymptotic dynamics of a damped wave equations on a time-dependent domains with homogeneous Dirichlet boundary condition, the nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. To this end, we establish the existence and uniqueness of strong and weak solutions satisfying energy inequality under the assumption that the spatial domains $\mathcal{O}_{t}$ in $\mathbb{R}^{3}$ are obtained from a bounded base domain $\mathcal{O}$ by a $C^{3}$-diffeomorphism $r(·, t)$. Furthermore, we establish the pullback attractor under a slightly weaker assumption that the measure of the spatial domains are uniformly bounded above.

Boundedness and global solvability to a chemotaxis-haptotaxis model with slow and fast diffusion
Chunhua Jin
2018, 23(4) : 1675-1688 doi: 10.3934/dcdsb.2018069 +[Abstract](402) +[HTML](339) +[PDF](434.52KB)
Abstract:

In this paper, we deal with the following coupled chemotaxis-haptotaxis system modeling cancer invasionwith nonlinear diffusion, where \begin{document} $Ω\subset\mathbb R^N$ \end{document} (\begin{document} $N≥ 3$ \end{document}) is a bounded domain. Under zero-flux boundary conditions, we showed that for any \begin{document} $m>0$ \end{document}, the problem admits a global bounded weak solution for any large initial datum if \begin{document} $\frac{χ}{μ}$ \end{document} is appropriately small. The slow diffusion case (\begin{document} $m>1$ \end{document}) of this problem have been studied by many authors [14,7,19,23], in which, the boundedness and the global in time solution are established for \begin{document} $m>\frac{2N}{N+2}$ \end{document}, but the cases \begin{document} $m≤ \frac{2N}{N+2}$ \end{document} remain open.

Asymptotic behavior of random fitzhugh-nagumo systems driven by colored noise
Anhui Gu and Bixiang Wang
2018, 23(4) : 1689-1720 doi: 10.3934/dcdsb.2018072 +[Abstract](541) +[HTML](591) +[PDF](550.74KB)
Abstract:

In this paper, we prove the existence and uniqueness of random attractors for the FitzHugh-Nagumo system driven by colored noise with a nonlinear diffusion term. We demonstrate that the colored noise is much easier to deal with than the white noise for studying the pathwise dynamics of stochastic systems. In addition, we show the attractors of the random FitzHugh-Nagumo system driven by a linear multiplicative colored noise converge to that of the corresponding stochastic system driven by a linear multiplicative white noise.

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](523) +[HTML](312) +[PDF](391.76KB)
Abstract:

In this paper, a diffusive prey-predator model with strong Allee effect growth rate and a protection zone $\Omega _0$ for the prey is investigated. We analyze the global existence, long time behaviors of positive solutions and the local stabilities of semi-trivial solutions. Moreover, the conditions of the occurrence and avoidance of overexploitation phenomenon are obtained. Furthermore, we demonstrate that the existence and stability of non-constant steady state solutions branching from constant semi-trivial solutions by using bifurcation theory. Our results show that the protection zone is effective when Allee threshold is small and the protection zone is large.

Laplace-Beltrami operator for the heat conduction in polymer coating of electronic devices
Micol Amar and Roberto Gianni
2018, 23(4) : 1739-1756 doi: 10.3934/dcdsb.2018078 +[Abstract](139) +[HTML](100) +[PDF](584.91KB)
Abstract:

In this paper we study a model for the heat conduction in a composite having a microscopic structure arranged in a periodic array. We obtain the macroscopic behaviour of the material and specifically the overall conductivity via an homogenization procedure, providing the equation satisfied by the effective temperature.

A regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity
Jishan Fan, Fucai Li and Gen Nakamura
2018, 23(4) : 1757-1766 doi: 10.3934/dcdsb.2018079 +[Abstract](107) +[HTML](81) +[PDF](346.78KB)
Abstract:

We establish a regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity and vacuum in a bounded domain.

Nonlocal elliptic system arising from the growth of cancer stem cells
Manuel Delgado, Ítalo Bruno Mendes Duarte and Antonio Suárez Fernández
2018, 23(4) : 1767-1795 doi: 10.3934/dcdsb.2018083 +[Abstract](129) +[HTML](86) +[PDF](641.08KB)
Abstract:

In this work we show the existence of coexistence states for a nonlocal elliptic system arising from the growth of cancer stem cells. For this, we use the bifurcation method and the theory of the fixed point index in cones. Moreover, in some cases we study the behaviour of the coexistence region, depending on the parameters of the problem.

Parking 3-sphere swimmer I. Energy minimizing strokes
François Alouges and Giovanni Di Fratta
2018, 23(4) : 1797-1817 doi: 10.3934/dcdsb.2018085 +[Abstract](95) +[HTML](76) +[PDF](1059.04KB)
Abstract:

The paper is about the parking 3-sphere swimmer (sPr3), a low-Reynolds number model swimmer composed of three balls of equal radii. The three balls can move along three horizontal axes (supported in the same plane) that mutually meet at the center of sPr3 with angles of 120°. The governing dynamical system is introduced and the implications of its geometric symmetries revealed. It is then shown that, in the first order range of small strokes, optimal periodic strokes are ellipses embedded in 3d space, i.e., closed curves of the form \begin{document} $t ∈ [0, 2 π] \mapsto (\cos t) u + (\sin t) v$ \end{document} for suitable vectors u and v of \begin{document} $\mathbb{R}^3$ \end{document}. A simple analytic expression for the vectors u and v is derived.

Singular perturbed renormalization group theory and its application to highly oscillatory problems
Wenlei Li and Shaoyun Shi
2018, 23(4) : 1819-1833 doi: 10.3934/dcdsb.2018089 +[Abstract](118) +[HTML](94) +[PDF](404.83KB)
Abstract:

Renormalization group method in the singular perturbation theory, originally introduced by Chen et al, has been proven to be very practicable in a large number of singular perturbed problems. In this paper, we will firstly reconsider the Renormalization group method under some general conditions to get several newly rigorous approximate results. Then we will apply the obtained results to investigate a class of second order differential equations with the highly oscillatory phenomenon of highly oscillatory properties, which occurs in many multiscale models from applied mathematics, physics and material science, etc. Our strategy, in fact, can be also used to analyze the same problem for related evolution equations with multiple scales, such as nonlinear Klein-Gordon equations in the nonrelativistic limit regime.

Determination of the area of exponential attraction in one-dimensional finite-time systems using meshless collocation
Peter Giesl and James McMichen
2018, 23(4) : 1835-1850 doi: 10.3934/dcdsb.2018094 +[Abstract](113) +[HTML](85) +[PDF](473.43KB)
Abstract:

We consider a non-autonomous ordinary differential equation over a finite time interval \begin{document}$[T_1,T_2]$\end{document}. The area of exponential attraction consists of solutions such that the distance to adjacent solutions exponentially contracts from \begin{document}$T_1$\end{document} to \begin{document}$T_2$\end{document}. One can use a contraction metric to determine an area of exponential attraction and to provide a bound on the rate of attraction.

In this paper, we will give the first method to algorithmically construct a contraction metric for finite-time systems in one spatial dimension. We will show the existence of a contraction metric, given by a function which satisfies a second-order partial differential equation with boundary conditions. We then use meshless collocation to approximately solve this equation, and show that the resulting approximation itself defines a contraction metric, if the collocation points are sufficiently dense. We give error estimates and apply the method to an example.

Stability and robustness analysis for a multispecies chemostat model with delays in the growth rates and uncertainties
Frederic Mazenc, Gonzalo Robledo and Michael Malisoff
2018, 23(4) : 1851-1872 doi: 10.3934/dcdsb.2018098 +[Abstract](157) +[HTML](78) +[PDF](550.22KB)
Abstract:

We study a chemostat model with an arbitrary number of competing species, one substrate, and constant dilution rates. We allow delays in the growth rates and additive uncertainties. Using constant inputs of certain species, we derive bounds on the sizes of the delays that ensure asymptotic stability of an equilibrium when the uncertainties are zero, which can allow persistence of multiple species. Under delays and uncertainties, we provide bounds on the delays and on the uncertainties that ensure input-to-state stability with respect to uncertainties.

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
2017doi: 10.3934/dcdsb.2017128 +[Abstract](724) +[HTML](321) +[PDF](463.5KB)
Predicting and estimating probability density functions of chaotic systems
Noah H. Rhee, Paweł Góra and Majid Bani-Yaghoub
2017doi: 10.3934/dcdsb.2017144 +[Abstract](559) +[HTML](297) +[PDF](463.5KB)
Macroalgal allelopathy in the emergence of coral diseases
Joydeb Bhattacharyya and Samares Pal
2017doi: 10.3934/dcdsb.2017146 +[Abstract](467) +[HTML](309) +[PDF](3327.2KB)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2017doi: 10.3934/dcdsb.2017149 +[Abstract](1029) +[HTML](446) +[PDF](547.3KB)
Stability of dislocation networks of low angle grain boundaries using a continuum energy formulation
Yang Xiang and Xiaodong Yan
2017doi: 10.3934/dcdsb.2017183 +[Abstract](491) +[HTML](311) +[PDF](634.8KB)
Positive symplectic integrators for predator-prey dynamics
Fasma Diele and Carmela Marangi
2017doi: 10.3934/dcdsb.2017185 +[Abstract](861) +[HTML](311) +[PDF](921.7KB)
Effect of perturbation in the numerical solution of fractional differential equations
Roberto Garrappa, Eleonora Messina and Antonia Vecchio
2017doi: 10.3934/dcdsb.2017188 +[Abstract](618) +[HTML](338) +[PDF](420.5KB)
On the scale dynamics of the tropical cyclone intensity
Chanh Kieu and Quan Wang
2017doi: 10.3934/dcdsb.2017196 +[Abstract](530) +[HTML](298) +[PDF](1342.2KB)
Repulsion effects on boundedness in a quasilinear attraction-repulsion chemotaxis model in higher dimensions
Hai-Yang Jin and Tian Xiang
2017doi: 10.3934/dcdsb.2017197 +[Abstract](575) +[HTML](316) +[PDF](443.0KB)
Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth
Giuseppe Viglialoro and Thomas E. Woolley
2017doi: 10.3934/dcdsb.2017199 +[Abstract](823) +[HTML](306) +[PDF](1131.4KB)
Positive steady states of a density-dependent predator-prey model with diffusion
Kaigang Huang, Yongli Cai, Feng Rao, Shengmao Fu and Weiming Wang
2017doi: 10.3934/dcdsb.2017209 +[Abstract](560) +[HTML](309) +[PDF](583.6KB)
Continuous and discrete one dimensional autonomous fractional ODEs
Yuanyuan Feng, Lei Li, Jian-Guo Liu and Xiaoqian Xu
2017doi: 10.3934/dcdsb.2017210 +[Abstract](591) +[HTML](274) +[PDF](598.6KB)
Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources
Julia Amador and Mariajesus Lopez-Herrero
2017doi: 10.3934/dcdsb.2017211 +[Abstract](632) +[HTML](300) +[PDF](361.2KB)
Method of sub-super solutions for fractional elliptic equations
Yanqin Fang and De Tang
2017doi: 10.3934/dcdsb.2017212 +[Abstract](524) +[HTML](285) +[PDF](367.5KB)
Analysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays
Shihe Xu, Meng Bai and Fangwei Zhang
2017doi: 10.3934/dcdsb.2017213 +[Abstract](493) +[HTML](300) +[PDF](390.7KB)
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
2017doi: 10.3934/dcdsb.2017214 +[Abstract](442) +[HTML](271) +[PDF](442.6KB)
A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential
Stefano Pasquali
2017doi: 10.3934/dcdsb.2017215 +[Abstract](405) +[HTML](272) +[PDF](488.0KB)
A space-time discontinuous Galerkin spectral element method for the Stefan problem
Chaoxu Pei, Mark Sussman and M. Yousuff Hussaini
2017doi: 10.3934/dcdsb.2017216 +[Abstract](613) +[HTML](294) +[PDF](935.4KB)
Transient growth in stochastic Burgers flows
Diogo Poças and Bartosz Protas
2017doi: 10.3934/dcdsb.2018052 +[Abstract](228) +[HTML](171) +[PDF](1189.23KB)
Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching
Zhenzhong Zhang, Enhua Zhang and Jinying Tong
2017doi: 10.3934/dcdsb.2018053 +[Abstract](226) +[HTML](166) +[PDF](528.62KB)
Asymptotic behavior of non-expanding piecewise linear maps in the presence of random noise
Fumihiko Nakamura
2017doi: 10.3934/dcdsb.2018055 +[Abstract](193) +[HTML](142) +[PDF](626.5KB)
A stochastic SIRI epidemic model with Lévy noise
Badr-eddine Berrhazi, Mohamed El Fatini, Tomás Caraballo and Roger Pettersson
2017doi: 10.3934/dcdsb.2018057 +[Abstract](441) +[HTML](261) +[PDF](2352.75KB)
Qualitative analysis of kinetic-based models for tumor-immune system interaction
Martina Conte, Maria Groppi and Giampiero Spiga
2017doi: 10.3934/dcdsb.2018060 +[Abstract](223) +[HTML](176) +[PDF](1014.89KB)
Mechanism for the color transition of the Belousov-Zhabotinsky reaction catalyzed by cerium ions and ferroin
Chikahiro Egami
2017doi: 10.3934/dcdsb.2018061 +[Abstract](309) +[HTML](291) +[PDF](1626.92KB)
Random dynamics of non-autonomous semi-linear degenerate parabolic equations on $\mathbb{R}^N$ driven by an unbounded additive noise
Wenqiang Zhao
2017doi: 10.3934/dcdsb.2018065 +[Abstract](195) +[HTML](158) +[PDF](518.34KB)
A new flexible discrete-time model for stable populations
Eduardo Liz
2017doi: 10.3934/dcdsb.2018066 +[Abstract](209) +[HTML](137) +[PDF](375.35KB)
The modified Camassa-Holm equation in Lagrangian coordinates
Yu Gao and Jian-Guo Liu
2017doi: 10.3934/dcdsb.2018067 +[Abstract](248) +[HTML](179) +[PDF](710.67KB)
Algebraic limit cycles for quadratic polynomial differential systems
Jaume Llibre and Claudia Valls
2017doi: 10.3934/dcdsb.2018070 +[Abstract](517) +[HTML](309) +[PDF](332.89KB)
On a coupled SDE-PDE system modeling acid-mediated tumor invasion
Sandesh Athni Hiremath, Christina Surulescu, Anna Zhigun and Stefanie Sonner
2017doi: 10.3934/dcdsb.2018071 +[Abstract](456) +[HTML](322) +[PDF](4078.93KB)
A new criterion to a two-chemical substances chemotaxis system with critical dimension
Xueli Bai and Suying Liu
2017doi: 10.3934/dcdsb.2018074 +[Abstract](378) +[HTML](364) +[PDF](331.56KB)
Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations
Mickaël D. Chekroun
2017doi: 10.3934/dcdsb.2018075 +[Abstract](376) +[HTML](302) +[PDF](707.16KB)
Extinction and coexistence of species for a diffusive intraguild predation model with B-D functional response
Guohong Zhang and Xiaoli Wang
2017doi: 10.3934/dcdsb.2018076 +[Abstract](106) +[HTML](97) +[PDF](695.95KB)
Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type
B. Ambrosio, M. A. Aziz-Alaoui and V. L. E. Phan
2017doi: 10.3934/dcdsb.2018077 +[Abstract](128) +[HTML](87) +[PDF](340.38KB)
Coexistence and extinction in Time-Periodic Volterra-Lotka type systems with nonlocal dispersal
Tung Nguyen and Nar Rawal
2017doi: 10.3934/dcdsb.2018080 +[Abstract](108) +[HTML](88) +[PDF](468.39KB)
A comparison of boundary correction methods for Strang splitting
Lukas Einkemmer and Alexander Ostermann
2017doi: 10.3934/dcdsb.2018081 +[Abstract](97) +[HTML](84) +[PDF](552.18KB)
A non-autonomous predator-prey model with infected prey
Yang Lu, Xia Wang and Shengqiang Liu
2017doi: 10.3934/dcdsb.2018082 +[Abstract](119) +[HTML](79) +[PDF](766.39KB)
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
2017doi: 10.3934/dcdsb.2018084 +[Abstract](118) +[HTML](77) +[PDF](467.51KB)
A locking free Reissner-Mindlin element with weak Galerkin rotations
Ruishu Wang, Lin Mu and Xiu Ye
2017doi: 10.3934/dcdsb.2018086 +[Abstract](115) +[HTML](82) +[PDF](367.32KB)
On the stability of $\vartheta$-methods for stochastic Volterra integral equations
Dajana Conte, Raffaele D'Ambrosio and Beatrice Paternoster
2017doi: 10.3934/dcdsb.2018087 +[Abstract](109) +[HTML](96) +[PDF](565.69KB)
Two-step collocation methods for fractional differential equations
Angelamaria Cardone, Dajana Conte and Beatrice Paternoster
2017doi: 10.3934/dcdsb.2018088 +[Abstract](151) +[HTML](80) +[PDF](447.88KB)
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
2017doi: 10.3934/dcdsb.2018090 +[Abstract](111) +[HTML](90) +[PDF](4796.31KB)
Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes
Qilong Zhai and Ran Zhang
2017doi: 10.3934/dcdsb.2018091 +[Abstract](97) +[HTML](87) +[PDF](351.95KB)
Pseudospectral reduction to compute Lyapunov exponents of delay differential equations
Dimitri Breda and Sara Della Schiava
2017doi: 10.3934/dcdsb.2018092 +[Abstract](136) +[HTML](91) +[PDF](1961.23KB)
Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces
Chao Deng and Tong Li
2017doi: 10.3934/dcdsb.2018093 +[Abstract](120) +[HTML](81) +[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
2017doi: 10.3934/dcdsb.2018095 +[Abstract](121) +[HTML](93) +[PDF](8917.37KB)
Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law
Zhiguo Xu, Weizhu Bao and Shaoyun Shi
2017doi: 10.3934/dcdsb.2018096 +[Abstract](88) +[HTML](86) +[PDF](821.2KB)
Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation
Aslihan Demirkaya and Milena Stanislavova
2017doi: 10.3934/dcdsb.2018097 +[Abstract](96) +[HTML](80) +[PDF](2559.58KB)
Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics
Naveen K. Vaidya, Xianping Li and Feng-Bin Wang
2017doi: 10.3934/dcdsb.2018099 +[Abstract](130) +[HTML](87) +[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
2017doi: 10.3934/dcdsb.2018100 +[Abstract](94) +[HTML](78) +[PDF](2817.98KB)
Periodic orbits of perturbed non-axially symmetric potentials in 1:1:1 and 1:1:2 resonances
Motserrat Corbera, Jaume Llibre and Claudia Valls
2017doi: 10.3934/dcdsb.2018101 +[Abstract](118) +[HTML](85) +[PDF](807.78KB)
Global regularity results for the climate model with fractional dissipation
Boqing Dong, Wenjuan Wang, Jiahong Wu and Hui Zhang
2017doi: 10.3934/dcdsb.2018102 +[Abstract](127) +[HTML](74) +[PDF](447.41KB)
Periodic orbits of planar discontinuous system under discretization
Luca Dieci, Timo Eirola and Cinzia Elia
2017doi: 10.3934/dcdsb.2018103 +[Abstract](117) +[HTML](80) +[PDF](1248.34KB)
Superconvergence of the semi-discrete local discontinuous Galerkin method for nonlinear KdV-type problems
Mahboub Baccouch
2017doi: 10.3934/dcdsb.2018104 +[Abstract](136) +[HTML](83) +[PDF](16469.35KB)
Numerical preservation of long-term dynamics by stochastic two-step methods
Raffaele D'Ambrosio, Martina Moccaldi and Beatrice Paternoster
2017doi: 10.3934/dcdsb.2018105 +[Abstract](110) +[HTML](78) +[PDF](310.59KB)
Partitioned second order method for magnetohydrodynamics in Elsässer variables
Yong Li and Catalin Trenchea
2017doi: 10.3934/dcdsb.2018106 +[Abstract](71) +[HTML](87) +[PDF](409.45KB)
An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model
Mahadevan Ganesh, Brandon C. Reyes and Avi Purkayastha
2017doi: 10.3934/dcdsb.2018107 +[Abstract](103) +[HTML](85) +[PDF](727.13KB)
Underlying one-step methods and nonautonomous stability of general linear methods
Andrew J. Steyer and Erik S. Van Vleck
2017doi: 10.3934/dcdsb.2018108 +[Abstract](121) +[HTML](94) +[PDF](447.38KB)
Two-grid finite element method for the stabilization of mixed Stokes-Darcy model
Jiaping Yu, Haibiao Zheng, Feng Shi and Ren Zhao
2017doi: 10.3934/dcdsb.2018109 +[Abstract](131) +[HTML](80) +[PDF](4434.43KB)
A comparative study on nonlocal diffusion operators related to the fractional Laplacian
Siwei Duo, Hong Wang and Yanzhi Zhang
2017doi: 10.3934/dcdsb.2018110 +[Abstract](112) +[HTML](101) +[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
2017doi: 10.3934/dcdsb.2018111 +[Abstract](152) +[HTML](87) +[PDF](4837.74KB)
Smooth to discontinuous systems: A geometric and numerical method for slow-fast dynamics
Luca Dieci and Cinzia Elia
2017doi: 10.3934/dcdsb.2018112 +[Abstract](144) +[HTML](82) +[PDF](6317.76KB)
The impact of releasing sterile mosquitoes on malaria transmission
Hongyan Yin, Cuihong Yang, Xin'an Zhang and Jia Li
2017doi: 10.3934/dcdsb.2018113 +[Abstract](62) +[HTML](38) +[PDF](487.02KB)
On one problem of viscoelastic fluid dynamics with memory on an infinite time interval
Victor Zvyagin and Vladimir Orlov
2017doi: 10.3934/dcdsb.2018114 +[Abstract](53) +[HTML](42) +[PDF](411.15KB)
On the initial boundary value problem of a Navier-Stokes/$Q$-tensor model for liquid crystals
Yuning Liu and Wei Wang
2017doi: 10.3934/dcdsb.2018115 +[Abstract](55) +[HTML](37) +[PDF](477.75KB)
Asymptotic spreading of time periodic competition diffusion systems
Wei-Jian Bo and Guo Lin
2017doi: 10.3934/dcdsb.2018116 +[Abstract](67) +[HTML](38) +[PDF](385.48KB)
Stationary solutions of neutral stochastic partial differential equations with delays in the highest-order derivatives
Kai Liu
2017doi: 10.3934/dcdsb.2018117 +[Abstract](46) +[HTML](35) +[PDF](448.16KB)
Dynamic transitions of the Fitzhugh-Nagumo equations on a finite domain
Yiqiu Mao
2017doi: 10.3934/dcdsb.2018118 +[Abstract](48) +[HTML](35) +[PDF](301.91KB)
Improved extensibility criteria and global well-posedness of a coupled chemotaxis-fluid model on bounded domains
Jishan Fan and Kun Zhao
2017doi: 10.3934/dcdsb.2018119 +[Abstract](43) +[HTML](38) +[PDF](440.38KB)
A multiscale model of the CD8 T cell immune response structured by intracellular content
Loïc Barbarroux, Philippe Michel, Mostafa Adimy and Fabien Crauste
2017doi: 10.3934/dcdsb.2018120 +[Abstract](49) +[HTML](107) +[PDF](1723.06KB)
Asymptotic decay for the classical solution of the chemotaxis system with fractional Laplacian in high dimensions
Xi Wang, Zuhan Liu and Ling Zhou
2017doi: 10.3934/dcdsb.2018121 +[Abstract](59) +[HTML](36) +[PDF](471.09KB)
Pullback attractors and invariant measures for discrete Klein-Gordon-Schrödinger equations
Caidi Zhao, Gang Xue and Grzegorz Łukaszewicz
2017doi: 10.3934/dcdsb.2018122 +[Abstract](55) +[HTML](36) +[PDF](562.27KB)
Fink type conjecture on affine-periodic solutions and Levinson's conjecture to Newtonian systems
Yong Li, Hongren Wang and Xue Yang
2017doi: 10.3934/dcdsb.2018123 +[Abstract](52) +[HTML](41) +[PDF](375.6KB)
Spatial dynamics of a reaction-diffusion cholera model with spatial heterogeneity
Xiaoyan Zhang and Yuxiang Zhang
2017doi: 10.3934/dcdsb.2018124 +[Abstract](59) +[HTML](57) +[PDF](382.16KB)
Analysis of a stage-structured dengue model
Jinping Fang, Guang Lin and Hui Wan
2017doi: 10.3934/dcdsb.2018125 +[Abstract](48) +[HTML](67) +[PDF](751.82KB)
Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity
Zhenguo Bai and Tingting Zhao
2017doi: 10.3934/dcdsb.2018126 +[Abstract](59) +[HTML](33) +[PDF](507.84KB)
Time asymptotics of structured populations with diffusion and dynamic boundary conditions
Mustapha Mokhtar-Kharroubi and Quentin Richard
2017doi: 10.3934/dcdsb.2018127 +[Abstract](56) +[HTML](44) +[PDF](448.24KB)
On a free boundary problem for a nonlocal reaction-diffusion model
Jia-Feng Cao, Wan-Tong Li and Meng Zhao
2017doi: 10.3934/dcdsb.2018128 +[Abstract](82) +[HTML](37) +[PDF](449.31KB)
Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor
Zejia Wang, Suzhen Xu and Huijuan Song
2017doi: 10.3934/dcdsb.2018129 +[Abstract](52) +[HTML](52) +[PDF](389.33KB)
Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ)
Hebai Chen and Xingwu Chen
2017doi: 10.3934/dcdsb.2018130 +[Abstract](46) +[HTML](57) +[PDF](1358.71KB)
On the Cauchy problem for the XFEL Schrödinger equation
Binhua Feng and Dun Zhao
2017doi: 10.3934/dcdsb.2018131 +[Abstract](59) +[HTML](38) +[PDF](393.67KB)
A perturbed fourth order elliptic equation with negative exponent
Zongming Guo and Long Wei
2017doi: 10.3934/dcdsb.2018132 +[Abstract](62) +[HTML](35) +[PDF](396.0KB)
Carleman estimate for solutions to a degenerate convection-diffusion equation
Chunpeng Wang, Yanan Zhou, Runmei Du and Qiang Liu
2017doi: 10.3934/dcdsb.2018133 +[Abstract](58) +[HTML](57) +[PDF](431.08KB)
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
2017doi: 10.3934/dcdsb.2018134 +[Abstract](69) +[HTML](36) +[PDF](1059.21KB)
Upper and lower bounds for the blow-up time in quasilinear reaction diffusion problems
Juntang Ding and Xuhui Shen
2017doi: 10.3934/dcdsb.2018135 +[Abstract](56) +[HTML](39) +[PDF](378.73KB)
Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources
Benlong Xu and Hongyan Jiang
2017doi: 10.3934/dcdsb.2018136 +[Abstract](61) +[HTML](40) +[PDF](353.5KB)
Dynamics of weak solutions for the three dimensional Navier-Stokes equations with nonlinear damping
Fang Li, Bo You and Yao Xu
2017doi: 10.3934/dcdsb.2018137 +[Abstract](58) +[HTML](48) +[PDF](470.16KB)
Exponential stability of an incompressible non-Newtonian fluid with delay
Linfang Liu, Tomás Caraballo and Xianlong Fu
2017doi: 10.3934/dcdsb.2018138 +[Abstract](67) +[HTML](60) +[PDF](543.28KB)
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](923) +[PDF](239.9KB) Cited By(101)
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](597) +[PDF](139.6KB) Cited By(91)
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](423) +[PDF](226.2KB) Cited By(70)
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](485) +[PDF](197.7KB) Cited By(61)
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](704) +[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](459) +[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](618) +[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](462) +[PDF](2040.6KB) Cited By(48)
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](421) +[PDF](181.0KB) Cited By(46)
Analysis of a phase field Navier-Stokes vesicle-fluid interaction model
Qiang Du, Manlin Li and Chun Liu
2007, 8(3) : 539-556 doi: 10.3934/dcdsb.2007.8.539 +[Abstract](483) +[PDF](207.8KB) 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
2017, 22(11) : 1-16 doi: 10.3934/dcdsb.2017128 +[Abstract](724) +[HTML](321) +[PDF](463.5KB) PDF Downloads(131)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2017, 22(11) : 1-22 doi: 10.3934/dcdsb.2017149 +[Abstract](1029) +[HTML](446) +[PDF](547.3KB) PDF Downloads(111)
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](609) +[HTML](131) +[PDF](690.66KB) PDF Downloads(110)
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](340) +[HTML](166) +[PDF](479.0KB) PDF Downloads(107)
Long-time behavior of a class of nonlocal partial differential equations
Chang Zhang, Fang Li and Jinqiao Duan
2018, 23(2) : 749-763 doi: 10.3934/dcdsb.2018041 +[Abstract](672) +[HTML](107) +[PDF](420.27KB) PDF Downloads(100)
In memoriam Igor D. Chueshov September 23, 1951 - April 23, 2016
Ludwig Arnold
2018, 23(3) : ⅰ-ⅸ doi: 10.3934/dcdsb.201803i +[Abstract](778) +[HTML](288) +[PDF](6684.8KB) PDF Downloads(99)
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](523) +[HTML](312) +[PDF](391.76KB) PDF Downloads(97)
Hopf bifurcation of an age-structured virus infection model
Hossein Mohebbi, Azim Aminataei, Cameron J. Browne and Mohammad Reza Razvan
2018, 23(2) : 861-885 doi: 10.3934/dcdsb.2018046 +[Abstract](558) +[HTML](127) +[PDF](794.93KB) PDF Downloads(81)
Robustness of time-dependent attractors in H1-norm for nonlocal problems
Tomás Caraballo, Marta Herrera-Cobos and Pedro Marín-Rubio
2018, 23(3) : 1011-1036 doi: 10.3934/dcdsb.2018140 +[Abstract](273) +[HTML](170) +[PDF](538.38KB) PDF Downloads(78)
How seasonal forcing influences the complexity of a predator-prey system
Xueping Li, Jingli Ren, Sue Ann Campbell, Gail S. K. Wolkowicz and Huaiping Zhu
2018, 23(2) : 785-807 doi: 10.3934/dcdsb.2018043 +[Abstract](926) +[HTML](140) +[PDF](4589.35KB) PDF Downloads(72)

2016  Impact Factor: 0.994

Editors

Referees

Librarians

Email Alert

[Back to Top]