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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.

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Preface: Special issue on dynamical systems on graphs
Stefan Siegmund and Petr Stehlík
2018, 23(5) : ⅰ-ⅲ doi: 10.3934/dcdsb.201805i +[Abstract](256) +[HTML](122) +[PDF](83.21KB)
Generalized network transport and Euler-Hille formula
Jacek Banasiak and Aleksandra Puchalska
2018, 23(5) : 1873-1893 doi: 10.3934/dcdsb.2018185 +[Abstract](227) +[HTML](97) +[PDF](495.1KB)

In this article we consider asymptotic properties of network flow models with fast transport along the edges and explore their connection with an operator version of the Euler formula for the exponential function. This connection, combined with the theory of the regular convergence of semigroups, allows for proving that for fast transport along the edges and slow rate of redistribution of the flow at the nodes, the network flow semigroup (or its suitable projection) can be approximated by a finite dimensional dynamical system related to the boundary conditions at the nodes of the network. The novelty of our results lies in considering more general boundary operators than that allowed for in previous papers.

On arbitrarily long periodic orbits of evolutionary games on graphs
Jeremias Epperlein and Vladimír Švígler
2018, 23(5) : 1895-1915 doi: 10.3934/dcdsb.2018187 +[Abstract](153) +[HTML](100) +[PDF](834.37KB)

A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. We construct graphs and corresponding initial conditions whose trajectories are periodic with an arbitrary minimal period length. We also examine a periodic behavior of evolutionary games on graphs with the underlying graph being an acyclic (tree) graph. Astonishingly, even this acyclic structure allows for arbitrary long periodic behavior.

Approximating network dynamics: Some open problems
Winfried Just
2018, 23(5) : 1917-1930 doi: 10.3934/dcdsb.2018188 +[Abstract](232) +[HTML](104) +[PDF](387.62KB)

Discrete-time finite-state dynamical systems on networks are often conceived as tractable approximations to more detailed ODE-based models of natural systems. Here we review research on a class of such discrete models $N$ that approximate certain ODE models $M$ of mathematical neuroscience. In particular, we outline several open problems on the dynamics of the models $N$ themselves, as well as on structural features of ODE models $M$ that allow for the construction of discrete approximations $N$ whose predictions will be consistent with those of $M$.

Explosive synchronization in mono and multilayer networks
Inmaculada Leyva, Irene Sendiña-Nadal and Stefano Boccaletti
2018, 23(5) : 1931-1944 doi: 10.3934/dcdsb.2018189 +[Abstract](137) +[HTML](136) +[PDF](2616.59KB)

Explosive synchronization, an abrupt transition to a collective coherent state, has been the focus of an extensive research since its first observation in scale-free networks with degree-frequency correlations. In this work, we report several scenarios where a first-order transition to synchronization occurs driven by the presence of a dependence between dynamics and network structure. Therefore, different mechanisms are shown to be able to prevent the formation of a giant synchronization cluster for sufficient large values of the coupling constant in both mono and multilayer networks. Using the Kuramoto model as a reference, we show how for an arbitrary network topology and frequency distribution, a very general weighting procedure acting on the weight of the links delays the synchronization transition forming independent synchronization clusters which suddenly merge above a critical threshold of the coupling constant. A completely different scenario in adaptive and multilayer networks is introduced which gives rise to the emergence of an explosive synchronization when a feedback between the dynamics and structure is operating by means of dependence links weighted through the order parameter.

Dynamical systems associated with adjacency matrices
Delio Mugnolo
2018, 23(5) : 1945-1973 doi: 10.3934/dcdsb.2018190 +[Abstract](126) +[HTML](88) +[PDF](562.08KB)

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss in detail qualitative properties of solutions to these problems by quadratic form methods. We distinguish between backward and forward evolution equations: the latter have typical features of diffusive processes, but cannot be well-posed on graphs with unbounded degree. On the contrary, well-posedness of backward equations is a typical feature of line graphs. We suggest how to detect even cycles and/or couples of odd cycles on graphs by studying backward equations for the adjacency matrix on their line graph.

Evolving multiplayer networks: Modelling the evolution of cooperation in a mobile population
Karan Pattni, Mark Broom and Jan Rychtář
2018, 23(5) : 1975-2004 doi: 10.3934/dcdsb.2018191 +[Abstract](120) +[HTML](79) +[PDF](786.29KB)

We consider a finite population of individuals that can move through a structured environment using our previously developed flexible evolutionary framework. In the current paper the behaviour of the individuals follows a Markov movement model where decisions about whether they should stay or leave depends upon the group of individuals they are with at present. The interaction between individuals is modelled using a public goods game. We demonstrate that cooperation can evolve when there is a cost associated with movement. Combining the movement cost with a larger population size has a positive effect on the evolution of cooperation. Moreover, increasing the exploration time, which is the amount of time an individual is allowed to explore its environment, also has a positive effect. Unusually, we find that the evolutionary dynamics used does not have a significant effect on these results.

On bounding exact models of epidemic spread on networks
Péter L. Simon and Istvan Z. Kiss
2018, 23(5) : 2005-2020 doi: 10.3934/dcdsb.2018192 +[Abstract](118) +[HTML](91) +[PDF](374.03KB)

In this paper we use comparison theorems from classical ODE theory in order to rigorously show that closures or approximations at individual or node level lead to mean-field models that bound the exact stochastic process from above. This will be done in the context of modelling epidemic spread on networks and the proof of the result relies on the observation that the epidemic process is negatively correlated (in the sense that the probability of an edge being in the susceptible-infected state is smaller than the product of the probabilities of the nodes being in the susceptible and infected states, respectively). The results in the paper hold for Markovian epidemics and arbitrary weighted and directed networks. Furthermore, we cast the results in a more general framework where alternative closures, other than that assuming the independence of nodes connected by an edge, are possible and provide a succinct summary of the stability analysis of the resulting more general mean-field models. While deterministic initial conditions are key to obtain the negative correlation result we show that this condition can be relaxed as long as extra conditions on the edge weights are imposed.

From coupled networks of systems to networks of states in phase space
Oskar Weinberger and Peter Ashwin
2018, 23(5) : 2021-2041 doi: 10.3934/dcdsb.2018193 +[Abstract](158) +[HTML](104) +[PDF](966.81KB)

Dynamical systems on graphs can show a wide range of behaviours beyond simple synchronization - even simple globally coupled structures can exhibit attractors with intermittent and slow switching between patterns of synchrony. Such attractors, called heteroclinic networks, can be well described as networks in phase space and in this paper we review some results and examples of how these robust attractors can be characterised from the synchrony properties and how coupled systems can be designed to exhibit given but arbitrary network attractors in phase space.

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](973) +[HTML](488) +[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](810) +[HTML](457) +[PDF](463.5KB)
Macroalgal allelopathy in the emergence of coral diseases
Joydeb Bhattacharyya and Samares Pal
2017doi: 10.3934/dcdsb.2017146 +[Abstract](672) +[HTML](461) +[PDF](3327.2KB)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2017doi: 10.3934/dcdsb.2017149 +[Abstract](1395) +[HTML](719) +[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](733) +[HTML](481) +[PDF](634.8KB)
Positive symplectic integrators for predator-prey dynamics
Fasma Diele and Carmela Marangi
2017doi: 10.3934/dcdsb.2017185 +[Abstract](1146) +[HTML](467) +[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](907) +[HTML](501) +[PDF](420.5KB)
On the scale dynamics of the tropical cyclone intensity
Chanh Kieu and Quan Wang
2017doi: 10.3934/dcdsb.2017196 +[Abstract](797) +[HTML](448) +[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](786) +[HTML](471) +[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](1145) +[HTML](461) +[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](765) +[HTML](463) +[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](844) +[HTML](440) +[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](893) +[HTML](452) +[PDF](361.2KB)
Method of sub-super solutions for fractional elliptic equations
Yanqin Fang and De Tang
2017doi: 10.3934/dcdsb.2017212 +[Abstract](776) +[HTML](419) +[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](732) +[HTML](453) +[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](643) +[HTML](418) +[PDF](442.6KB)
A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential
Stefano Pasquali
2017doi: 10.3934/dcdsb.2017215 +[Abstract](631) +[HTML](412) +[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](840) +[HTML](455) +[PDF](935.4KB)
Transient growth in stochastic Burgers flows
Diogo Poças and Bartosz Protas
2017doi: 10.3934/dcdsb.2018052 +[Abstract](425) +[HTML](344) +[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](438) +[HTML](335) +[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](358) +[HTML](292) +[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](701) +[HTML](441) +[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](420) +[HTML](333) +[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](582) +[HTML](552) +[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](374) +[HTML](296) +[PDF](518.34KB)
A new flexible discrete-time model for stable populations
Eduardo Liz
2017doi: 10.3934/dcdsb.2018066 +[Abstract](420) +[HTML](277) +[PDF](375.35KB)
The modified Camassa-Holm equation in Lagrangian coordinates
Yu Gao and Jian-Guo Liu
2017doi: 10.3934/dcdsb.2018067 +[Abstract](444) +[HTML](320) +[PDF](710.67KB)
Algebraic limit cycles for quadratic polynomial differential systems
Jaume Llibre and Claudia Valls
2017doi: 10.3934/dcdsb.2018070 +[Abstract](731) +[HTML](461) +[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](678) +[HTML](488) +[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](562) +[HTML](523) +[PDF](331.56KB)
Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations
Mickaël D. Chekroun
2017doi: 10.3934/dcdsb.2018075 +[Abstract](576) +[HTML](446) +[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](272) +[HTML](258) +[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](315) +[HTML](238) +[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](268) +[HTML](244) +[PDF](468.39KB)
A comparison of boundary correction methods for Strang splitting
Lukas Einkemmer and Alexander Ostermann
2017doi: 10.3934/dcdsb.2018081 +[Abstract](258) +[HTML](233) +[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](323) +[HTML](236) +[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](300) +[HTML](234) +[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](283) +[HTML](221) +[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](307) +[HTML](254) +[PDF](565.69KB)
Two-step collocation methods for fractional differential equations
Angelamaria Cardone, Dajana Conte and Beatrice Paternoster
2017doi: 10.3934/dcdsb.2018088 +[Abstract](360) +[HTML](228) +[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](316) +[HTML](247) +[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](274) +[HTML](225) +[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](310) +[HTML](257) +[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](304) +[HTML](239) +[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](294) +[HTML](247) +[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](246) +[HTML](226) +[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](280) +[HTML](235) +[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](343) +[HTML](240) +[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](269) +[HTML](287) +[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](307) +[HTML](247) +[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](298) +[HTML](219) +[PDF](447.41KB)
Periodic orbits of planar discontinuous system under discretization
Luca Dieci, Timo Eirola and Cinzia Elia
2017doi: 10.3934/dcdsb.2018103 +[Abstract](286) +[HTML](228) +[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](319) +[HTML](233) +[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](285) +[HTML](216) +[PDF](310.59KB)
Partitioned second order method for magnetohydrodynamics in Elsässer variables
Yong Li and Catalin Trenchea
2017doi: 10.3934/dcdsb.2018106 +[Abstract](237) +[HTML](239) +[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](299) +[HTML](233) +[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](354) +[HTML](240) +[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](402) +[HTML](236) +[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](295) +[HTML](324) +[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](387) +[HTML](248) +[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](352) +[HTML](235) +[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](258) +[HTML](190) +[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](228) +[HTML](185) +[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](229) +[HTML](176) +[PDF](477.75KB)
Asymptotic spreading of time periodic competition diffusion systems
Wei-Jian Bo and Guo Lin
2017doi: 10.3934/dcdsb.2018116 +[Abstract](246) +[HTML](177) +[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](200) +[HTML](190) +[PDF](448.16KB)
Dynamic transitions of the Fitzhugh-Nagumo equations on a finite domain
Yiqiu Mao
2017doi: 10.3934/dcdsb.2018118 +[Abstract](245) +[HTML](194) +[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](203) +[HTML](184) +[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](241) +[HTML](278) +[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](248) +[HTML](195) +[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](261) +[HTML](177) +[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](223) +[HTML](184) +[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](243) +[HTML](247) +[PDF](382.16KB)
Analysis of a stage-structured dengue model
Jinping Fang, Guang Lin and Hui Wan
2017doi: 10.3934/dcdsb.2018125 +[Abstract](219) +[HTML](255) +[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](270) +[HTML](205) +[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](247) +[HTML](188) +[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](265) +[HTML](182) +[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](206) +[HTML](196) +[PDF](389.33KB)
Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ)
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