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


In memoriam Igor D. Chueshov September 23, 1951 - April 23, 2016
Ludwig Arnold
2018, 23(3) : ⅰ-ⅸ doi: 10.3934/dcdsb.201803i +[Abstract](214) +[HTML](77) +[PDF](6684.8KB)
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](100) +[HTML](61) +[PDF](479.0KB)

The well-posedness and asymptotic dynamics of second-order-in-time stochastic evolution equations with state-dependent delay is investigated. This class covers several important stochastic PDE models arising in the theory of nonlinear plates with additive noise. We first prove well-posedness in a certain space of functions which are \begin{document}$C^1$\end{document} in time. The solutions constructed generate a random dynamical system in a \begin{document}$C^1$\end{document}-type space over the delay time interval. Our main result shows that this random dynamical system possesses compact global and exponential attractors of finite fractal dimension. To obtain this result we adapt the recently developed method of quasi-stability estimates to the random setting.

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](82) +[HTML](60) +[PDF](538.38KB)

In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H1-norm are analysed for a parameterized family of non-autonomous nonlocal reaction-diffusion equations without uniqueness, improving previous results [Nonlinear Dyn. 84 (2016), 35-50].

Long-time dynamics of vectorial von Karman system with nonlinear thermal effects and free boundary conditions
Irena Lasiecka, To Fu Ma and Rodrigo Nunes Monteiro
2018, 23(3) : 1037-1072 doi: 10.3934/dcdsb.2018141 +[Abstract](124) +[HTML](65) +[PDF](661.21KB)

This paper is concerned with long-time dynamics of a full von Karman system subject to nonlinear thermal coupling and free boundary conditions. In contrast with scalar von Karman system, vectorial full von Karman system accounts for both vertical and in plane displacements. The corresponding PDE is of critical interest in flow structure interactions where nonlinear plate/shell dynamics interacts with perturbed flows [vicid or invicid] [8,9,15]. In this paper it is shown that the system admits a global attractor which is also smooth and of finite fractal dimension. The above result is shown to hold for plates without regularizing effects of rotational inertia and without any mechanical dissipation imposed on vertical displacements. This is in contrast with the literature on this topic [15] and references therein. In order to handle highly supercritical nature of the von Karman nonlinearities, new results on "hidden" trace regularity generated by thermal effects are exploited. These lead to asymptotic compensated compactness of trajectories which then allows to use newly developed tools pertaining to quasi stable dynamical systems [8].

On the time evolution of Bernstein processes associated with a class of parabolic equations
Pierre-A. Vuillermot
2018, 23(3) : 1073-1090 doi: 10.3934/dcdsb.2018142 +[Abstract](87) +[HTML](57) +[PDF](426.62KB)

In this article dedicated to the memory of Igor D. Chueshov, I first summarize in a few words the joint results that we obtained over a period of six years regarding the long-time behavior of solutions to a class of semilinear stochastic parabolic partial differential equations. Then, as the beautiful interplay between partial differential equations and probability theory always was close to Igor's heart, I present some new results concerning the time evolution of certain Markovian Bernstein processes naturally associated with a class of deterministic linear parabolic partial differential equations. Particular instances of such processes are certain conditioned Ornstein-Uhlenbeck processes, generalizations of Bernstein bridges and Bernstein loops, whose laws may evolve in space in a non trivial way. Specifically, I examine in detail the time development of the probability of finding such processes within two-dimensional geometric shapes exhibiting spherical symmetry. I also define a Faedo-Galerkin scheme whose ultimate goal is to allow approximate computations with controlled error terms of the various probability distributions involved.

Viral infection model with diffusion and state-dependent delay: Stability of classical solutions
Alexander Rezounenko
2018, 23(3) : 1091-1105 doi: 10.3934/dcdsb.2018143 +[Abstract](89) +[HTML](59) +[PDF](491.0KB)

A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are interested in classical solutions with Lipschitz in-time initial functions which are adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions technique is used to analyse stability of interior infection equilibria which describe the cases of a chronic disease.

Feedback stabilization of a linear hydro-elastic system
Lorena Bociu, Steven Derochers and Daniel Toundykov
2018, 23(3) : 1107-1132 doi: 10.3934/dcdsb.2018144 +[Abstract](83) +[HTML](59) +[PDF](561.58KB)

It is known that the linear Stokes-Lamé system can be stabilized by a boundary feedback in the form of a dissipative velocity matching on the common interface [5]. Here we consider feedback stabilization for a generalized linear fluid-elasticity interaction, where the matching conditions on the interface incorporate the curvature of the common boundary and thus take into account the geometry of the problem. Such a coupled system is semigroup well-posed on the natural finite energy space [13], however, the system is not dissipative to begin with, which represents a key departure from the feedback control analysis in [5]. We prove that a damped version of the general linear hydro-elasticity model is exponentially stable. First, such a result is given for boundary dissipation of the form used in [5]. This proof resolves a more complex version, compared to the classical case, of the weighted energy methods, and addresses the lack of over-determination in the associated unique continuation result. The second theorem demonstrates how assumptions can be relaxed if a viscous damping is added in the interior of the solid.

Homogenization of trajectory attractors of Ginzburg-Landau equations with randomly oscillating terms
Gregory A. Chechkin, Vladimir V. Chepyzhov and Leonid S. Pankratov
2018, 23(3) : 1133-1154 doi: 10.3934/dcdsb.2018145 +[Abstract](87) +[HTML](58) +[PDF](748.1KB)

We consider complex Ginzburg-Landau (GL) type equations of the form:

where \begin{document}$R$\end{document}, \begin{document}$β$\end{document}, and \begin{document}$g$\end{document} are random rapidly oscillating real functions. Assuming that the random functions are ergodic and statistically homogeneous in space variables, we prove that the trajectory attractors of these systems tend to the trajectory attractors of the homogenized equations whose terms are the average of the corresponding terms of the initial systems.

Bibliography: 52 titles.

Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows
Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero and Michael Z. Zgurovsky
2018, 23(3) : 1155-1176 doi: 10.3934/dcdsb.2018146 +[Abstract](91) +[HTML](56) +[PDF](501.19KB)

In this paper we prove the existence of global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of complex fluids. We also show that the attractors tend to the set of all complete bounded trajectories of the original problem when the parameter of the approximations goes to zero.

Generalized KdV equation subject to a stochastic perturbation
Annie Millet and Svetlana Roudenko
2018, 23(3) : 1177-1198 doi: 10.3934/dcdsb.2018147 +[Abstract](86) +[HTML](59) +[PDF](460.63KB)

We prove global well-posedness of the subcritical generalized Korteweg-de Vries equation (the mKdV and the gKdV with quartic power of nonlinearity) subject to an additive random perturbation. More precisely, we prove that if the driving noise is a cylindrical Wiener process on \begin{document} $L^2(\mathbb{R})$ \end{document} and the covariance operator is Hilbert-Schmidt in an appropriate Sobolev space, then the solutions with \begin{document} $H^1(\mathbb{R})$ \end{document} initial data are globally well-posed in \begin{document} $H^1(\mathbb{R})$ \end{document}. This extends results obtained by A. de Bouard and A. Debussche for the stochastic KdV equation.

Random Delta-Hausdorff-attractors
Michael Scheutzow and Maite Wilke-Berenguer
2018, 23(3) : 1199-1217 doi: 10.3934/dcdsb.2018148 +[Abstract](76) +[HTML](59) +[PDF](458.85KB)

Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate concepts: Δ-Hausdorff-attractors are characterized by attracting all deterministic compact sets of Hausdorff dimension at most Δ, where Δ is a non-negative number, while cc-attractors attract all countable compact sets. We provide two examples showing that a given random dynamical system may have various different Δ-Hausdorff-attractors for different values of Δ. It seems that both concepts are new even in the context of deterministic dynamical systems.

On the Oseledets-splitting for infinite-dimensional random dynamical systems
Kening Lu, Alexandra Neamţu and Björn Schmalfuss
2018, 23(3) : 1219-1242 doi: 10.3934/dcdsb.2018149 +[Abstract](87) +[HTML](55) +[PDF](457.73KB)

We investigate the Oseledets splitting for Banach space-valued random dynamical systems based on the theory of center manifolds. This technique gives us random one-dimensional invariant spaces which turn out to be the Oseledets subspaces under suitable assumptions. We apply these results to a stochastic parabolic evolution equation driven by a fractional Brownian motion.

Long time behaviour of strong solutions to interactive fluid-plate system without rotational inertia
Iryna Ryzhkova-Gerasymova
2018, 23(3) : 1243-1265 doi: 10.3934/dcdsb.2018150 +[Abstract](84) +[HTML](54) +[PDF](484.35KB)

We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier-Stokes equations in a bounded domain and a classical (nonlinear) full von Karman plate equations that accounts for both transversal and lateral displacements on a flexible part of the boundary. Rotational inertia of the filaments of the plate is not taken into account. Our main result shows well-posedness of strong solutions to the problem, thus the problem generates a semiflow in an appropriate phase space. We also prove uniform stability of strong solutions to homogeneous problem.

Semigroup well-posedness of a linearized, compressible fluid with an elastic boundary
George Avalos, Pelin G. Geredeli and Justin T. Webster
2018, 23(3) : 1267-1295 doi: 10.3934/dcdsb.2018151 +[Abstract](83) +[HTML](56) +[PDF](640.14KB)

We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the compressible Navier-Stokes equations about an arbitrary state (assuming the fluid is barotropic), and so the fluid PDE component of the interaction will generally include a nontrivial ambient flow profile \begin{document}$\mathbf{U}$\end{document}. The appearance of this term introduces new challenges at the level of the stationary problem. In addition, the boundary of the fluid domain is unavoidably Lipschitz, and so the well-posedness argument takes into account the technical issues associated with obtaining necessary boundary trace and elliptic regularity estimates. Much of the previous work on flow-plate models was done via Galerkin-type constructions after obtaining good a priori estimates on solutions (specifically [18]-the work most pertinent to ours here); in contrast, we adopt here a Lumer-Phillips approach, with a view of associating solutions of the fluid-structure dynamics with a \begin{document}$C_{0}$\end{document}-semigroup \begin{document}${{\left\{ {{e}^{\mathcal{A}t}} \right\}}_{t\ge 0}}$\end{document} on the natural finite energy space of initial data. So, given this approach, the major challenge in our work becomes establishing the maximality of the operator \begin{document}$\mathcal{A}$\end{document} that models the fluid-structure dynamics. In sum: our main result is semigroup well-posedness for the fully coupled fluid-structure dynamics, under the assumption that the ambient flow field \begin{document}$ \mathbf{U}∈ \mathbf{H}^{3}(\mathcal{O})$\end{document} has zero normal component trace on the boundary (a standard assumption with respect to the literature). In the final sections we address well-posedness of the system in the presence of the von Karman plate nonlinearity, as well as the stationary problem associated to the dynamics.

Squeezing and finite dimensionality of cocycle attractors for 2D stochastic Navier-Stokes equation with non-autonomous forcing
Hongyong Cui, Mirelson M. Freitas and José A. Langa
2018, 23(3) : 1297-1324 doi: 10.3934/dcdsb.2018152 +[Abstract](136) +[HTML](57) +[PDF](521.33KB)

In this paper, we study the squeezing property and finite dimensionality of cocycle attractors for non-autonomous dynamical systems (NRDS). We show that the generalized random cocycle squeezing property (RCSP) is a sufficient condition to prove a determining modes result and the finite dimensionality of invariant non-autonomous random sets, where the upper bound of the dimension is uniform for all components of the invariant set. We also prove that the RCSP can imply the pullback flattening property in uniformly convex Banach space so that could also contribute to establish the asymptotic compactness of the system. The cocycle attractor for 2D Navier-Stokes equation with additive white noise and translation bounded non-autonomous forcing is studied as an application.

Global stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers
Varga K. Kalantarov and Edriss S. Titi
2018, 23(3) : 1325-1345 doi: 10.3934/dcdsb.2018153 +[Abstract](88) +[HTML](63) +[PDF](436.17KB)

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping term, the Benjamin-Bona-Mahony-Burgers equation and the KdV-Burgers equation. This algorithm capitalizes on the fact that such infinite-dimensional dissipative dynamical systems posses finite-dimensional long-time behavior which is represented by, for instance, the finitely many determining parameters of their long-time dynamics, such as determining Fourier modes, determining volume elements, determining nodes, etc..The algorithm utilizes these finite parameters in the form of feedback control to stabilize the relevant solutions. For the sake of clarity, and in order to fix ideas, we focus in this work on the case of low Fourier modes feedback controller, however, our results and tools are equally valid for using other feedback controllers employing other spatial coarse mesh interpolants.

Loss of derivatives for hyperbolic boundary problems with constant coefficients
Matthias Eller
2018, 23(3) : 1347-1361 doi: 10.3934/dcdsb.2018154 +[Abstract](75) +[HTML](55) +[PDF](389.81KB)

Symmetric hyperbolic systems and constantly hyperbolic systems with constant coefficients and a boundary condition which satisfies a weakened form of the Kreiss-Sakamoto condition are considered. A well-posedness result is established which generalizes a theorem by Chazarain and Piriou for scalar strictly hyperbolic equations and non-characteristic boundaries [3]. The proof is based on an explicit solution of the boundary problem by means of the Fourier-Laplace transform. As long as the operator is symmetric, the boundary is allowed to be characteristic.

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](539) +[HTML](221) +[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](376) +[HTML](203) +[PDF](463.5KB)
Macroalgal allelopathy in the emergence of coral diseases
Joydeb Bhattacharyya and Samares Pal
2017doi: 10.3934/dcdsb.2017146 +[Abstract](343) +[HTML](195) +[PDF](3327.2KB)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2017doi: 10.3934/dcdsb.2017149 +[Abstract](787) +[HTML](294) +[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](359) +[HTML](200) +[PDF](634.8KB)
Positive symplectic integrators for predator-prey dynamics
Fasma Diele and Carmela Marangi
2017doi: 10.3934/dcdsb.2017185 +[Abstract](665) +[HTML](207) +[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](410) +[HTML](226) +[PDF](420.5KB)
On the scale dynamics of the tropical cyclone intensity
Chanh Kieu and Quan Wang
2017doi: 10.3934/dcdsb.2017196 +[Abstract](333) +[HTML](189) +[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](430) +[HTML](201) +[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](622) +[HTML](204) +[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](404) +[HTML](206) +[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](380) +[HTML](183) +[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](465) +[HTML](203) +[PDF](361.2KB)
Method of sub-super solutions for fractional elliptic equations
Yanqin Fang and De Tang
2017doi: 10.3934/dcdsb.2017212 +[Abstract](363) +[HTML](201) +[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](312) +[HTML](188) +[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](284) +[HTML](175) +[PDF](442.6KB)
A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential
Stefano Pasquali
2017doi: 10.3934/dcdsb.2017215 +[Abstract](273) +[HTML](178) +[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](461) +[HTML](208) +[PDF](935.4KB)
Transient growth in stochastic Burgers flows
Diogo Poças and Bartosz Protas
2017doi: 10.3934/dcdsb.2018052 +[Abstract](84) +[HTML](59)
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](83) +[HTML](67)
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
2017doi: 10.3934/dcdsb.2018054 +[Abstract](80) +[HTML](64) +[PDF](661.21KB)
Asymptotic behavior of non-expanding piecewise linear maps in the presence of random noise
Fumihiko Nakamura
2017doi: 10.3934/dcdsb.2018055 +[Abstract](74) +[HTML](57) +[PDF](426.62KB)
Time fractional and space nonlocal stochastic boussinesq equations driven by gaussian white noise
Tianlong Shen, Jianhua Huang and Caibin Zeng
2017doi: 10.3934/dcdsb.2018056 +[Abstract](82) +[HTML](60) +[PDF](491.0KB)
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](188) +[HTML](100) +[PDF](560.96KB)
Longtime robustness and semi-uniform compactness of a pullback attractor via nonautonomous PDE
Yangrong Li, Lianbing She and Jinyan Yin
2017doi: 10.3934/dcdsb.2018058 +[Abstract](95) +[HTML](65) +[PDF](748.1KB)
Dynamics of a Lotka-Volterra competition-diffusion model with stage structure and spatial heterogeneity
Shuling Yan and Shangjiang Guo
2017doi: 10.3934/dcdsb.2018059 +[Abstract](102) +[HTML](73)
Qualitative analysis of kinetic-based models for tumor-immune system interaction
Martina Conte, Maria Groppi and Giampiero Spiga
2017doi: 10.3934/dcdsb.2018060 +[Abstract](72) +[HTML](59)
Mechanism for the color transition of the Belousov-Zhabotinsky reaction catalyzed by cerium ions and ferroin
Chikahiro Egami
2017doi: 10.3934/dcdsb.2018061 +[Abstract](145) +[HTML](131) +[PDF](458.85KB)
Two codimension-two bifurcations of a second-order difference equation from macroeconomics
Jiyu Zhong and Shengfu Deng
2017doi: 10.3934/dcdsb.2018062 +[Abstract](89) +[HTML](69)
Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations
Katherine A. Kime
2017doi: 10.3934/dcdsb.2018063 +[Abstract](85) +[HTML](82) +[PDF](484.34KB)
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
2017doi: 10.3934/dcdsb.2018064 +[Abstract](69) +[HTML](62) +[PDF](640.14KB)
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](73) +[HTML](59) +[PDF](521.42KB)
A new flexible discrete-time model for stable populations
Eduardo Liz
2017doi: 10.3934/dcdsb.2018066 +[Abstract](70) +[HTML](56)
The modified Camassa-Holm equation in Lagrangian coordinates
Yu Gao and Jian-Guo Liu
2017doi: 10.3934/dcdsb.2018067 +[Abstract](107) +[HTML](83) +[PDF](389.81KB)
Dynamics for the damped wave equations on time-dependent domains
Feng Zhou, Chunyou Sun and Xin Li
2017doi: 10.3934/dcdsb.2018068 +[Abstract](287) +[HTML](185) +[PDF](601.14KB)
Boundedness and global solvability to a chemotaxis-haptotaxis model with slow and fast diffusion
Chunhua Jin
2017doi: 10.3934/dcdsb.2018069 +[Abstract](259) +[HTML](242) +[PDF](422.48KB)
Algebraic limit cycles for quadratic polynomial differential systems
Jaume Llibre and Claudia Valls
2017doi: 10.3934/dcdsb.2018070 +[Abstract](332) +[HTML](211) +[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](257) +[HTML](216) +[PDF](4078.93KB)
Asymptotic behavior of random Fitzhugh-Nagumo systems driven by colored noise
Anhui Gu and Bixiang Wang
2017doi: 10.3934/dcdsb.2018072 +[Abstract](332) +[HTML](417) +[PDF](530.98KB)
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
2017doi: 10.3934/dcdsb.2018073 +[Abstract](352) +[HTML](209) +[PDF](372.59KB)
A new criterion to a two-chemical substances chemotaxis system with critical dimension
Xueli Bai and Suying Liu
2017doi: 10.3934/dcdsb.2018074 +[Abstract](259) +[HTML](262) +[PDF](331.56KB)
Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations
Mickaël D. Chekroun
2017doi: 10.3934/dcdsb.2018075 +[Abstract](249) +[HTML](188) +[PDF](707.16KB)
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](553) +[PDF](239.9KB) Cited By(99)
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](410) +[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](279) +[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](313) +[PDF](197.7KB) Cited By(61)
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](312) +[PDF](264.3KB) Cited By(59)
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](518) +[PDF](596.7KB) Cited By(58)
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](421) +[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](317) +[PDF](2040.6KB) Cited By(47)
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](308) +[PDF](207.8KB) 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](277) +[PDF](181.0KB) Cited By(45)
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](539) +[HTML](221) +[PDF](463.5KB) PDF Downloads(95)
Fractional Navier-Stokes equations
Jan W. Cholewa and Tomasz Dlotko
2017, 22(11) : 1-22 doi: 10.3934/dcdsb.2017149 +[Abstract](787) +[HTML](294) +[PDF](547.3KB) PDF Downloads(83)
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
2017, 22(11) : 1-17 doi: 10.3934/dcdsb.2018073 +[Abstract](352) +[HTML](209) +[PDF](372.59KB) PDF Downloads(62)
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](432) +[HTML](55) +[PDF](690.66KB) PDF Downloads(61)
A unifying approach to discrete single-species populations models
James Sandefur
2018, 23(2) : 493-508 doi: 10.3934/dcdsb.2017194 +[Abstract](424) +[HTML](65) +[PDF](666.76KB) PDF Downloads(54)
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](515) +[HTML](42) +[PDF](420.27KB) PDF Downloads(53)
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](399) +[HTML](44) +[PDF](794.93KB) PDF Downloads(53)
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](730) +[HTML](52) +[PDF](4589.35KB) PDF Downloads(52)
Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal
Guo-Bao Zhang, Ruyun Ma and Xue-Shi Li
2018, 23(2) : 587-608 doi: 10.3934/dcdsb.2018035 +[Abstract](370) +[HTML](47) +[PDF](472.19KB) PDF Downloads(46)
Asymptotic behavior of random Fitzhugh-Nagumo systems driven by colored noise
Anhui Gu and Bixiang Wang
2017, 22(11) : 1-32 doi: 10.3934/dcdsb.2018072 +[Abstract](332) +[HTML](417) +[PDF](530.98KB) PDF Downloads(43)

2016  Impact Factor: 0.994




Email Alert

[Back to Top]