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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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Singular perturbations and scaling
Christian Lax and Sebastian Walcher
2020, 25(1) : 1-29 doi: 10.3934/dcdsb.2019170 +[Abstract](668) +[HTML](267) +[PDF](509.58KB)
Quasi-periodic solutions for a class of beam equation system
Yanling Shi and Junxiang Xu
2020, 25(1) : 31-53 doi: 10.3934/dcdsb.2019171 +[Abstract](649) +[HTML](290) +[PDF](537.72KB)
Pullback exponential attractors for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping
Fang Li and Bo You
2020, 25(1) : 55-80 doi: 10.3934/dcdsb.2019172 +[Abstract](540) +[HTML](225) +[PDF](502.76KB)
Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment
Chengxia Lei, Jie Xiong and Xinhui Zhou
2020, 25(1) : 81-98 doi: 10.3934/dcdsb.2019173 +[Abstract](627) +[HTML](292) +[PDF](429.14KB)
Detailed analytic study of the compact pairwise model for SIS epidemic propagation on networks
Noémi Nagy and Péter L. Simon
2020, 25(1) : 99-115 doi: 10.3934/dcdsb.2019174 +[Abstract](357) +[HTML](188) +[PDF](489.47KB)
Stochastic partial differential equation models for spatially dependent predator-prey equations
Nhu N. Nguyen and George Yin
2020, 25(1) : 117-139 doi: 10.3934/dcdsb.2019175 +[Abstract](489) +[HTML](267) +[PDF](495.74KB)
Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries
Shuang Liu and Xinfeng Liu
2020, 25(1) : 141-159 doi: 10.3934/dcdsb.2019176 +[Abstract](466) +[HTML](239) +[PDF](526.55KB)
Some remarks on the Robust Stackelberg controllability for the heat equation with controls on the boundary
Víctor Hernández-Santamaría and Liliana Peralta
2020, 25(1) : 161-190 doi: 10.3934/dcdsb.2019177 +[Abstract](373) +[HTML](207) +[PDF](616.26KB)
Boundedness and stabilization in a two-species chemotaxis system with two chemicals
Liangchen Wang, Jing Zhang, Chunlai Mu and Xuegang Hu
2020, 25(1) : 191-221 doi: 10.3934/dcdsb.2019178 +[Abstract](474) +[HTML](238) +[PDF](627.66KB)
Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness
Zhiming Liu and Zhijian Yang
2020, 25(1) : 223-240 doi: 10.3934/dcdsb.2019179 +[Abstract](480) +[HTML](232) +[PDF](433.95KB)
Analytical formula and dynamic profile of mRNA distribution
Feng Jiao, Jian Ren and Jianshe Yu
2020, 25(1) : 241-257 doi: 10.3934/dcdsb.2019180 +[Abstract](349) +[HTML](223) +[PDF](630.88KB)
Analysis of time-domain Maxwell's equations in biperiodic structures
Gang Bao, Bin Hu, Peijun Li and Jue Wang
2020, 25(1) : 259-286 doi: 10.3934/dcdsb.2019181 +[Abstract](458) +[HTML](276) +[PDF](521.27KB)
Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay
Ya Wang, Fuke Wu, Xuerong Mao and Enwen Zhu
2020, 25(1) : 287-300 doi: 10.3934/dcdsb.2019182 +[Abstract](395) +[HTML](275) +[PDF](377.66KB)
Pullback exponential attractors for differential equations with variable delays
Mohamed Ali Hammami, Lassaad Mchiri, Sana Netchaoui and Stefanie Sonner
2020, 25(1) : 301-319 doi: 10.3934/dcdsb.2019183 +[Abstract](495) +[HTML](228) +[PDF](428.51KB)
Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution
Na An, Chaobao Huang and Xijun Yu
2020, 25(1) : 321-334 doi: 10.3934/dcdsb.2019185 +[Abstract](257) +[HTML](142) +[PDF](499.89KB)
Multi-scale analysis for highly anisotropic parabolic problems
Thomas Blanc and Mihaï Bostan
2020, 25(1) : 335-399 doi: 10.3934/dcdsb.2019186 +[Abstract](177) +[HTML](87) +[PDF](752.03KB)
Bi-center problem and Hopf cyclicity of a Cubic Liénard system
Min Hu, Tao Li and Xingwu Chen
2020, 25(1) : 401-414 doi: 10.3934/dcdsb.2019187 +[Abstract](209) +[HTML](120) +[PDF](1778.6KB)
A nonlinear fourth-order PDE for multi-frame image super-resolution enhancement
Amine Laghrib, Abdelkrim Chakib, Aissam Hadri and Abdelilah Hakim
2020, 25(1) : 415-442 doi: 10.3934/dcdsb.2019188 +[Abstract](1485) +[HTML](204) +[PDF](6444.21KB)
A hybrid model of collective motion of discrete particles under alignment and continuum chemotaxis
Ezio Di Costanzo, Marta Menci, Eleonora Messina, Roberto Natalini and Antonia Vecchio
2020, 25(1) : 443-472 doi: 10.3934/dcdsb.2019189 +[Abstract](221) +[HTML](181) +[PDF](1021.95KB)
On the forward dynamical behavior of nonautonomous systems
Chunqiu Li, Desheng Li and Xuewei Ju
2020, 25(1) : 473-487 doi: 10.3934/dcdsb.2019190 +[Abstract](312) +[HTML](114) +[PDF](403.87KB)
On the 1D modeling of fluid flowing through a Junction
Rinaldo M. Colombo and Mauro Garavello
2019doi: 10.3934/dcdsb.2019149 +[Abstract](331) +[HTML](219) +[PDF](537.93KB)
Derivation of cable equation by multiscale analysis for a model of myelinated axons
Carlos Jerez-Hanckes, Irina Pettersson and Volodymyr Rybalko
2019doi: 10.3934/dcdsb.2019191 +[Abstract](234) +[HTML](103) +[PDF](497.18KB)
Input-to-state stability of continuous-time systems via finite-time Lyapunov functions
Huijuan Li and Junxia Wang
2019doi: 10.3934/dcdsb.2019192 +[Abstract](237) +[HTML](86) +[PDF](525.25KB)
On steady state of some Lotka-Volterra competition-diffusion-advection model
Qi Wang
2019doi: 10.3934/dcdsb.2019193 +[Abstract](210) +[HTML](119) +[PDF](400.69KB)
Global dynamics of a reaction-diffusion system with intraguild predation and internal storage
Hua Nie, Sze-Bi Hsu and Feng-Bin Wang
2019doi: 10.3934/dcdsb.2019194 +[Abstract](238) +[HTML](110) +[PDF](1042.02KB)
The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems
Emma D'Aniello and Saber Elaydi
2019doi: 10.3934/dcdsb.2019195 +[Abstract](197) +[HTML](124) +[PDF](800.33KB)
Complete dynamical analysis for a nonlinear HTLV-I infection model with distributed delay, CTL response and immune impairment
Lianwen Wang, Zhijun Liu, Yong Li and Dashun Xu
2019doi: 10.3934/dcdsb.2019196 +[Abstract](219) +[HTML](171) +[PDF](368.83KB)
The global attractor for a class of extensible beams with nonlocal weak damping
Chunxiang Zhao, Chunyan Zhao and Chengkui Zhong
2019doi: 10.3934/dcdsb.2019197 +[Abstract](194) +[HTML](103) +[PDF](453.84KB)
Global existence for a two-phase flow model with cross-diffusion
Esther S. Daus, Josipa-Pina Milišić and Nicola Zamponi
2019doi: 10.3934/dcdsb.2019198 +[Abstract](206) +[HTML](104) +[PDF](527.48KB)
Spreading speed of a degenerate and cooperative epidemic model with free boundaries
Meng Zhao, Wan-Tong Li and Wenjie Ni
2019doi: 10.3934/dcdsb.2019199 +[Abstract](211) +[HTML](122) +[PDF](398.54KB)
Poxvirus, red and grey squirrel dynamics: Is the recovery of a common predator affecting system equilibria? Insights from a predator-prey ecoepidemic model
Elena Travaglia, Valentina La Morgia and Ezio Venturino
2019doi: 10.3934/dcdsb.2019200 +[Abstract](241) +[HTML](144) +[PDF](1246.27KB)
Takens–Bogdanov singularity for age structured models
Zhihua Liu and Rong Yuan
2019doi: 10.3934/dcdsb.2019201 +[Abstract](182) +[HTML](113) +[PDF](370.84KB)
A two-group age of infection epidemic model with periodic behavioral changes
Mamadou L. Diagne, Ousmane Seydi and Aissata A. B. Sy
2019doi: 10.3934/dcdsb.2019202 +[Abstract](214) +[HTML](99) +[PDF](552.81KB)
The operating diagram for a model of competition in a chemostat with an external lethal inhibitor
Bachir Bar and Tewfik Sari
2019doi: 10.3934/dcdsb.2019203 +[Abstract](269) +[HTML](114) +[PDF](1495.79KB)
A discrete model of competing species sharing a parasite
Rafael Bravo De La Parra and Luis Sanz
2019doi: 10.3934/dcdsb.2019204 +[Abstract](206) +[HTML](93) +[PDF](560.87KB)
Chaotic cuttlesh: king of camouage with self-excited and hidden flows, its fractional-order form and communication designs with fractional form
Karthikeyan Rajagopal, Serdar Cicek, Akif Akgul, Sajad Jafari and Anitha Karthikeyan
2019doi: 10.3934/dcdsb.2019205 +[Abstract](264) +[HTML](136) +[PDF](5631.2KB)
A dynamic model of the limit order book
Alberto Bressan, Marco Mazzola and Hongxu Wei
2019doi: 10.3934/dcdsb.2019206 +[Abstract](214) +[HTML](113) +[PDF](360.34KB)
A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior
Yuan Wu, Jin Liang and Bei Hu
2019doi: 10.3934/dcdsb.2019207 +[Abstract](244) +[HTML](115) +[PDF](373.55KB)
Emergent collective behaviors of stochastic kuramoto oscillators
Seung-Yeal Ha, Dongnam Ko, Chanho Min and Xiongtao Zhang
2019doi: 10.3934/dcdsb.2019208 +[Abstract](205) +[HTML](109) +[PDF](389.15KB)
Singularity formation to the two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction in a bounded domain
Xin Zhong
2019doi: 10.3934/dcdsb.2019209 +[Abstract](196) +[HTML](109) +[PDF](368.75KB)
Homoclinic orbits and chaos in the generalized Lorenz system
Ting Yang
2019doi: 10.3934/dcdsb.2019210 +[Abstract](265) +[HTML](136) +[PDF](321.93KB)
The fast signal diffusion limit in nonlinear chemotaxis systems
Marcel Freitag
2019doi: 10.3934/dcdsb.2019211 +[Abstract](217) +[HTML](142) +[PDF](410.12KB)
Global asymptotic stability of nonconvex sweeping processes
Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov and Oleg Makarenkov
2019doi: 10.3934/dcdsb.2019212 +[Abstract](243) +[HTML](117) +[PDF](664.24KB)
Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion
Bin Pei, Yong Xu and Yuzhen Bai
2019doi: 10.3934/dcdsb.2019213 +[Abstract](270) +[HTML](161) +[PDF](352.17KB)
Global stability of the predator-prey model with a sigmoid functional response
Yinshu Wu and Wenzhang Huang
2019doi: 10.3934/dcdsb.2019214 +[Abstract](287) +[HTML](131) +[PDF](258.16KB)
Existence and blow up of solutions to the $ 2D $ Burgers equation with supercritical dissipation
Binbin Shi and Weike Wang
2019doi: 10.3934/dcdsb.2019215 +[Abstract](241) +[HTML](111) +[PDF](409.8KB)
Existence of a global attractor for fractional differential hemivariational inequalities
Yirong Jiang, Nanjing Huang and Zhouchao Wei
2019doi: 10.3934/dcdsb.2019216 +[Abstract](216) +[HTML](179) +[PDF](397.98KB)
Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the zakharov equations
José R. Quintero and Juan C. Cordero
2019doi: 10.3934/dcdsb.2019217 +[Abstract](192) +[HTML](113) +[PDF](412.53KB)
Attractors for first order lattice systems with almost periodic nonlinear part
Ahmed Y. Abdallah
2019doi: 10.3934/dcdsb.2019218 +[Abstract](194) +[HTML](98) +[PDF](388.47KB)
A criterion for the existence of relaxation oscillations with applications to predator-prey systems and an epidemic model
Ting-Hao Hsu and Gail S. K. Wolkowicz
2019doi: 10.3934/dcdsb.2019219 +[Abstract](236) +[HTML](120) +[PDF](929.29KB)
On regularity of stochastic convolutions of functional linear differential equations with memory
Kai Liu
2019doi: 10.3934/dcdsb.2019220 +[Abstract](207) +[HTML](98) +[PDF](365.77KB)
Existence of pullback attractors for the non-autonomous suspension bridge equation with time delay
Suping Wang and Qiaozhen Ma
2019doi: 10.3934/dcdsb.2019221 +[Abstract](249) +[HTML](110) +[PDF](335.16KB)
Spreading speeds of rabies with territorial and diffusing rabid foxes
Khalaf M. Alanazi, Zdzislaw Jackiewicz and Horst R. Thieme
2019doi: 10.3934/dcdsb.2019222 +[Abstract](262) +[HTML](124) +[PDF](843.94KB)
Spatial spread of epidemic diseases in geographical settings: Seasonal influenza epidemics in Puerto Rico
Pierre Magal, Glenn F. Webb and Yixiang Wu
2019doi: 10.3934/dcdsb.2019223 +[Abstract](220) +[HTML](123) +[PDF](3937.7KB)
Density dependent replicator-mutator models in directed evolution
Matthieu Alfaro and Mario Veruete
2019doi: 10.3934/dcdsb.2019224 +[Abstract](176) +[HTML](103) +[PDF](709.37KB)
Slow convergence to equilibrium for an evolutionary epidemiology integro-differential system
Jean-Baptiste Burie, Ramsès Djidjou-Demasse and Arnaud Ducrot
2019doi: 10.3934/dcdsb.2019225 +[Abstract](242) +[HTML](119) +[PDF](448.18KB)
Global dynamics of an age-structured model with relapse
Mohammed Nor Frioui, Tarik Mohammed Touaoula and Bedreddine Ainseba
2019doi: 10.3934/dcdsb.2019226 +[Abstract](279) +[HTML](147) +[PDF](686.84KB)
Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions
Zhihua Liu and Pierre Magal
2019doi: 10.3934/dcdsb.2019227 +[Abstract](250) +[HTML](109) +[PDF](372.62KB)
Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms
Yoshikazu Giga, Hiroyoshi Mitake and Hung V. Tran
2019doi: 10.3934/dcdsb.2019228 +[Abstract](249) +[HTML](120) +[PDF](337.84KB)
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](3321) +[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](3022) +[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](2443) +[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](2718) +[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](3348) +[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](2587) +[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](3266) +[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](2363) +[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](1924) +[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](2344) +[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](6642) +[HTML](713) +[PDF](481.89KB) PDF Downloads(335)
The averaging method for multivalued SDEs with jumps and non-Lipschitz coefficients
Wei Mao, Liangjian Hu, Surong You and Xuerong Mao
2019, 24(9) : 4937-4954 doi: 10.3934/dcdsb.2019039 +[Abstract](1687) +[HTML](447) +[PDF](433.24KB) PDF Downloads(319)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2018, 23(8) : 2967-2988 doi: 10.3934/dcdsb.2017149 +[Abstract](5078) +[HTML](1097) +[PDF](566.06KB) PDF Downloads(318)
Global existence and stability in a two-species chemotaxis system
Huanhuan Qiu and Shangjiang Guo
2019, 24(4) : 1569-1587 doi: 10.3934/dcdsb.2018220 +[Abstract](2583) +[HTML](732) +[PDF](1079.83KB) PDF Downloads(266)
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](3415) +[HTML](620) +[PDF](519.85KB) PDF Downloads(246)
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](3137) +[HTML](525) +[PDF](488.66KB) PDF Downloads(243)
A stochastic SIRI epidemic model with Lévy noise
Badr-eddine Berrhazi, Mohamed El Fatini, Tomás Caraballo and Roger Pettersson
2018, 23(6) : 2415-2431 doi: 10.3934/dcdsb.2018057 +[Abstract](4831) +[HTML](796) +[PDF](2371.8KB) PDF Downloads(231)
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](3560) +[HTML](571) +[PDF](474.87KB) PDF Downloads(218)
Existence and uniqueness of solutions of free boundary problems in heterogeneous environments
Mingxin Wang
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Stability analysis of a chemotherapy model with delays
Ismail Abdulrashid, Abdallah A. M. Alsammani and Xiaoying Han
2019, 24(3) : 989-1005 doi: 10.3934/dcdsb.2019002 +[Abstract](2220) +[HTML](144) +[PDF](543.61KB) PDF Downloads(203)

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