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Sharp interface limit in a phase field model of cell motility

Networks and Heterogeneous Media  Volume 12, Issue 4, Pages : 551 - 590, 2017

Leonid Berlyand - (email), Mykhailo Potomkin - (email), Volodymyr Rybalko - (email)

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Traveling wave solutions of a reaction-diffusion predator-prey model

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 5, Pages : 1063 - 1078, 2017

Jiang Liu - (email), Xiaohui Shang - (email), Zengji Du - (email)

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3

On the modeling of transport phenomena in continuum and statistical mechanics

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 6, Pages : 1393 - 1411, 2017

Paolo Podio-Guidugli - (email)

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Smooth and non-smooth regularizations of the nonlinear diffusion equation

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 6, Pages : 1519 - 1537, 2017

Giuseppe Tomassetti - (email)

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5

Traveling waves in a three species competition-cooperation system

Communications on Pure and Applied Analysis  Volume 16, Issue 4, Pages : 1103 - 1119, 2017

Xiaojie Hou - (email), Yi Li - (email)

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Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system

Discrete and Continuous Dynamical Systems  Volume 37, Issue 5, Pages : 2813 - 2827, 2017

Chin-Chin Wu - (email)

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7

A proton therapy model using discrete difference equations with an example of treating hepatocellular carcinoma

Mathematical Biosciences and Engineering  Volume 14, Issue 4, Pages : 881 - 899, 2017

Erin N. Bodine - (email), K. Lars Monia - (email)

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8

Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 895 - 911, 2017

Chengxia Lei - (email), Yihong Du - (email)

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9

Lumpability of linear evolution equations in Banach spaces

Evolution Equations and Control Theory  Volume 6, Issue 1, Pages : 15 - 34, 2016

Fatihcan M. Atay - (email), Lavinia Roncoroni - (email)

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10

Transboundary capital and pollution flows and the emergence of regional inequalities

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 913 - 922, 2016

Simon Levin - (email), Anastasios Xepapadeas - (email)

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Numerical study of a particle method for gradient flows

Kinetic and Related Models  Volume 10, Issue 3, Pages : 613 - 641, 2016

José Antonio Carrillo - (email), Yanghong Huang - (email), Francesco Saverio Patacchini - (email), Gershon Wolansky - (email)

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12

Aggregated steady states of a kinetic model for chemotaxis

Kinetic and Related Models  Volume 10, Issue 1, Pages : 313 - 327, 2016

Anne Nouri - (email), Christian Schmeiser - (email)

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13

On the mathematical modelling of cellular (discontinuous) precipitation

Discrete and Continuous Dynamical Systems  Volume 37, Issue 2, Pages : 963 - 982, 2016

Oliver Penrose - (email)

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14

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Mathematical Biosciences and Engineering  Volume 14, Issue 2, Pages : 491 - 509, 2016

Tuoi Vo - (email), William Lee - (email), Adam Peddle - (email), Martin Meere - (email)

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15

On the symmetry of spatially periodic two-dimensional water waves

Discrete and Continuous Dynamical Systems  Volume 36, Issue 12, Pages : 7057 - 7061, 2016

Florian Kogelbauer - (email)

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16

Information diffusion in social sensing

Numerical Algebra, Control and Optimization  Volume 6, Issue 3, Pages : 365 - 411, 2016

Vikram Krishnamurthy - (email), William Hoiles - (email)

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17

Nonlinear diffusion equations in fluid mixtures

Evolution Equations and Control Theory  Volume 5, Issue 3, Pages : 431 - 448, 2016

Angelo Morro - (email)

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An accurate and efficient discrete formulation of aggregation population balance equation

Kinetic and Related Models  Volume 9, Issue 2, Pages : 373 - 391, 2016

Jitendra Kumar - (email), Gurmeet Kaur - (email), Evangelos Tsotsas - (email)

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19

Stability of interacting traveling waves in reaction-convection-diffusion systems

DCDS Supplements  Volume 2015, Issue special, Pages : 258 - 266, 2015

Grigori Chapiro - (email), Lucas Furtado - (email), Dan Marchesin - (email), Stephen Schecter - (email)

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20

Structured populations with diffusion and Feller conditions

Mathematical Biosciences and Engineering  Volume 13, Issue 2, Pages : 261 - 279, 2015

Agnieszka Bartłomiejczyk - (email), Henryk Leszczyński - (email)

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Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation

Discrete and Continuous Dynamical Systems  Volume 36, Issue 5, Pages : 2473 - 2496, 2015

Grégory Faye - (email)

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22

Protection zone in a modified Lotka-Volterra model

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 7, Pages : 2027 - 2038, 2015

Xiao He - (email), Sining Zheng - (email)

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A free boundary problem for aggregation by short range sensing and differentiated diffusion

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 5, Pages : 1461 - 1480, 2015

Jan Haškovec - (email), Dietmar Oelz - (email)

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24

Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions

Mathematical Biosciences and Engineering  Volume 12, Issue 4, Pages : 699 - 715, 2015

Lin Wang - (email), James Watmough - (email), Fang Yu - (email)

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25

Aggregation and environmental transmission in chronic wasting disease

Mathematical Biosciences and Engineering  Volume 12, Issue 1, Pages : 209 - 231, 2014

Olga Vasilyeva - (email), Tamer Oraby - (email), Frithjof Lutscher - (email)

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26

Modelling with measures: Approximation of a mass-emitting object by a point source

Mathematical Biosciences and Engineering  Volume 12, Issue 2, Pages : 357 - 373, 2014

Joep H.M. Evers - (email), Sander C. Hille - (email), Adrian Muntean - (email)

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Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations

Kinetic and Related Models  Volume 7, Issue 4, Pages : 713 - 737, 2014

Rajesh Kumar - (email), Jitendra Kumar - (email), Gerald Warnecke - (email)

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28

Traveling waves of a mutualistic model of mistletoes and birds

Discrete and Continuous Dynamical Systems  Volume 35, Issue 4, Pages : 1743 - 1765, 2014

Chuncheng Wang - (email), Rongsong Liu - (email), Junping Shi - (email), Carlos Martinez del Rio - (email)

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Effects of dispersal in a non-uniform environment on population dynamics and competition: A patch model approach

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 10, Pages : 3087 - 3104, 2014

Donald L. DeAngelis - (email), Bo Zhang - (email)

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Evolutionarily stable diffusive dispersal

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 10, Pages : 3319 - 3340, 2014

Alex Potapov - (email), Ulrike E. Schlägel - (email), Mark A. Lewis - (email)

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31

Singularly perturbed population models with reducible migration matrix 1. Sova-Kurtz theorem and the convergence to the aggregated model

Discrete and Continuous Dynamical Systems  Volume 35, Issue 2, Pages : 617 - 635, 2014

Jacek Banasiak - (email), Amartya Goswami - (email)

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32

Effect of intracellular diffusion on current--voltage curves in potassium channels

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 7, Pages : 1837 - 1853, 2014

Daniele Andreucci - (email), Dario Bellaveglia - (email), Emilio N.M. Cirillo - (email), Silvia Marconi - (email)

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33

Two-stage model of carcinogenic mutations with the influence of delays

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 8, Pages : 2501 - 2519, 2014

Urszula Foryś - (email), Beata Zduniak - (email)

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34

Phase transition and diffusion among socially interacting self-propelled agents

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 5, Pages : 1249 - 1278, 2014

Alethea B. T. Barbaro - (email), Pierre Degond - (email)

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35

A continuous phenotype space model of RNA virus evolution within a host

Mathematical Biosciences and Engineering  Volume 11, Issue 4, Pages : 919 - 927, 2014

Andrei Korobeinikov - (email), Conor Dempsey - (email)

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36

Steady-states and traveling-wave solutions of the generalized Constantin--Lax--Majda equation

Discrete and Continuous Dynamical Systems  Volume 34, Issue 8, Pages : 3155 - 3170, 2014

Hisashi Okamoto - (email), Takashi Sakajo - (email), Marcus Wunsch - (email)

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37

Optimal control of a diffusion/reaction/switching system

Evolution Equations and Control Theory  Volume 2, Issue 4, Pages : 723 - 731, 2013

Thomas I. Seidman - (email)

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38

Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models

Networks and Heterogeneous Media  Volume 8, Issue 3, Pages : 745 - 772, 2013

Benjamin Seibold - (email), Morris R. Flynn - (email), Aslan R. Kasimov - (email), Rodolfo R. Rosales - (email)

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39

Spreading speed and traveling waves for a two-species weak competition system with free boundary

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 9, Pages : 2441 - 2455, 2013

Chang-Hong Wu - (email)

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40

Existence and linear stability of solutions of the ballistic VSC model

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 1, Pages : 35 - 51, 2013

Joost Hulshof - (email), Robert Nolet - (email), Georg Prokert - (email)

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41

Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge

Mathematical Biosciences and Engineering  Volume 10, Issue 4, Pages : 979 - 996, 2013

Xiaoyuan Chang - (email), Junjie Wei - (email)

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42

A simple model of carcinogenic mutations with time delay and diffusion

Mathematical Biosciences and Engineering  Volume 10, Issue 3, Pages : 861 - 872, 2013

Monika Joanna Piotrowska - (email), Urszula Foryś - (email), Marek Bodnar - (email), Jan Poleszczuk - (email)

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43

A relaxation method for one dimensional traveling waves of singular and nonlocal equations

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 5, Pages : 1459 - 1491, 2013

Weiran Sun - (email), Min Tang - (email)

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44

Competition of motile and immotile bacterial strains in a petri dish

Mathematical Biosciences and Engineering  Volume 10, Issue 2, Pages : 399 - 424, 2013

Silogini Thanarajah - (email), Hao Wang - (email)

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45

Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations

Discrete and Continuous Dynamical Systems  Volume 33, Issue 8, Pages : 3567 - 3582, 2013

Armengol Gasull - (email), Hector Giacomini - (email), Joan Torregrosa - (email)

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46

On a reaction-diffusion model for sterile insect release method with release on the boundary

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 7, Pages : 2509 - 2522, 2012

Xin Li - (email), Xingfu Zou - (email)

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47

A Lattice model on somitogenesis of zebrafish

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 8, Pages : 2789 - 2814, 2012

Kang-Ling Liao - (email), Chih-Wen Shih - (email)

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48

Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 8, Pages : 2829 - 2848, 2012

Naveen K. Vaidya - (email), Feng-Bin Wang - (email), Xingfu Zou - (email)

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Spreading speeds and traveling waves for non-cooperative integro-difference systems

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 6, Pages : 2243 - 2266, 2012

Haiyan Wang - (email), Carlos Castillo-Chavez - (email)

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50

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 5, Pages : 1455 - 1471, 2012

Pavel Chigansky - (email), Fima C. Klebaner - (email)

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51

Multi-dimensional traveling fronts in bistable reaction-diffusion equations

Discrete and Continuous Dynamical Systems  Volume 32, Issue 3, Pages : 1011 - 1046, 2011

Masaharu Taniguchi - (email)

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52

A congestion model for cell migration

Communications on Pure and Applied Analysis  Volume 11, Issue 1, Pages : 243 - 260, 2011

Julien Dambrine - (email), Nicolas Meunier - (email), Bertrand Maury - (email), Aude Roudneff-Chupin - (email)

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53

Traveling wave solution for a lattice dynamical system with convolution type nonlinearity

Discrete and Continuous Dynamical Systems  Volume 32, Issue 1, Pages : 101 - 124, 2011

Jong-Shenq Guo - (email), Ying-Chih Lin - (email)

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54

Effects of spatial structure and diffusion on the performances of the chemostat

Mathematical Biosciences and Engineering  Volume 8, Issue 4, Pages : 953 - 971, 2011

Ihab Haidar - (email), Alain Rapaport - (email), Frédéric Gérard - (email)

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55

Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology

Discrete and Continuous Dynamical Systems - Series B  Volume 16, Issue 3, Pages : 895 - 925, 2011

Judith R. Miller - (email), Huihui Zeng - (email)

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56

Existence of traveling wavefront for discrete bistable competition model

Discrete and Continuous Dynamical Systems - Series B  Volume 16, Issue 3, Pages : 973 - 984, 2011

Chin-Chin Wu - (email)

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57

Physiologically structured populations with diffusion and dynamic boundary conditions

Mathematical Biosciences and Engineering  Volume 8, Issue 2, Pages : 503 - 513, 2011

József Z. Farkas - (email), Peter Hinow - (email)

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58

Traveling waves in Fermi-Pasta-Ulam lattices with saturable nonlinearities

Discrete and Continuous Dynamical Systems  Volume 30, Issue 3, Pages : 835 - 849, 2011

Alexander Pankov - (email), Vassilis M. Rothos - (email)

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59

Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations

Discrete and Continuous Dynamical Systems  Volume 30, Issue 1, Pages : 137 - 167, 2011

Aaron Hoffman - (email), Benjamin Kennedy - (email)

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60

Modelling phase transitions via Young measures

Discrete and Continuous Dynamical Systems - Series S  Volume 5, Issue 1, Pages : 29 - 48, 2011

Steffen Arnrich - (email)

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61

Traveling waves and their stability in a coupled reaction diffusion system

Communications on Pure and Applied Analysis  Volume 10, Issue 1, Pages : 141 - 160, 2010

Xiaojie Hou - (email), Wei Feng - (email)

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Traveling wave solutions for Lotka-Volterra system re-visited

Discrete and Continuous Dynamical Systems - Series B  Volume 15, Issue 1, Pages : 171 - 196, 2010

Anthony W. Leung - (email), Xiaojie Hou - (email), Wei Feng - (email)

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63

Global wellposedness and blowup of solutions to a nonlocal evolution problem with singular kernels

Communications on Pure and Applied Analysis  Volume 9, Issue 6, Pages : 1591 - 1606, 2010

Dong Li - (email), Xiaoyi Zhang - (email)

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Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion

Communications on Pure and Applied Analysis  Volume 9, Issue 6, Pages : 1617 - 1637, 2010

Andrea L. Bertozzi - (email), Dejan Slepcev - (email)

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65

Zero, one and two-switch models of gene regulation

Discrete and Continuous Dynamical Systems - Series B  Volume 14, Issue 2, Pages : 495 - 513, 2010

Somkid Intep - (email), Desmond J. Higham - (email)

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On a nonlocal aggregation model with nonlinear diffusion

Discrete and Continuous Dynamical Systems  Volume 27, Issue 1, Pages : 301 - 323, 2010

Dong Li - (email), Xiaoyi Zhang - (email)

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Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice

Discrete and Continuous Dynamical Systems - Series B  Volume 13, Issue 3, Pages : 559 - 575, 2010

Cui-Ping Cheng - (email), Wan-Tong Li - (email), Zhi-Cheng Wang - (email)

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Front propagation for a two-dimensional periodic monostable lattice dynamical system

Discrete and Continuous Dynamical Systems  Volume 26, Issue 1, Pages : 197 - 223, 2009

Jong-Shenq Guo - (email), Chang-Hong Wu - (email)

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Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities

Discrete and Continuous Dynamical Systems  Volume 26, Issue 1, Pages : 265 - 290, 2009

Xiaojie Hou - (email), Yi Li - (email), Kenneth R. Meyer - (email)

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Dependence of propagation speed on invader species: The effect of the predatory commensalism in two-prey, one-predator system with diffusion

Discrete and Continuous Dynamical Systems - Series B  Volume 12, Issue 4, Pages : 797 - 825, 2009

Sungrim Seirin Lee - (email)

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71

Some remarks on traveling wave solutions in competition models

Discrete and Continuous Dynamical Systems - Series B  Volume 12, Issue 2, Pages : 389 - 399, 2009

Bingtuan Li - (email)

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72

Stability, bifurcation analysis in a neural network model with delay and diffusion

DCDS Supplements  Volume 2009, Issue Special, Pages : 367 - 376, 2009

Rui Hu - (email), Yuan Yuan - (email)

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73

The two-dimensional Keller-Segel model after blow-up

Discrete and Continuous Dynamical Systems  Volume 25, Issue 1, Pages : 109 - 121, 2009

Jean Dolbeault - (email), Christian Schmeiser - (email)

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Spatial spread of sexually transmitted diseases within susceptible populations at demographic steady state

Mathematical Biosciences and Engineering  Volume 5, Issue 4, Pages : 713 - 727, 2008

Carlos Castillo-Chavez - (email), Bingtuan Li - (email)

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75

Global dynamics in a self--consistent model of elliptical galaxy

Discrete and Continuous Dynamical Systems - Series B  Volume 10, Issue 2/3, September, Pages : 439 - 454, 2008

Pablo Cincotta - (email), Claudia Giordano - (email), Juan C. Muzzio - (email)

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76

Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes

Discrete and Continuous Dynamical Systems - Series B  Volume 9, Issue 1, Pages : 47 - 64, 2007

Graeme D. Chalmers - (email), Desmond J. Higham - (email)

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77

Traveling waves to a reaction-diffusion equation

DCDS Supplements  Volume 2007, Issue Special, Pages : 382 - 390, 2007

Zhaosheng Feng - (email)

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78

Positive steady state of a food chain system with diffusion

DCDS Supplements  Volume 2007, Issue Special, Pages : 667 - 676, 2007

Jing Liu - (email), Xiaodong Liu - (email), Sining Zheng - (email), Yanping Lin - (email)

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79

An age and spatially structured model of tumor invasion with haptotaxis

Discrete and Continuous Dynamical Systems - Series B  Volume 8, Issue 1, Pages : 45 - 60, 2007

Janet Dyson - (email), Eva Sánchez - (email), Rosanna Villella-Bressan - (email), Glenn F. Webb - (email)

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80

Approximate solution of the Burgers-Korteweg-de Vries equation

Communications on Pure and Applied Analysis  Volume 6, Issue 2, Pages : 429 - 440, 2007

Zhaosheng Feng - (email), Yu Huang - (email)

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81

An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems

Mathematical Biosciences and Engineering  Volume 4, Issue 2, Pages : 187 - 203, 2007

Chichia Chiu - (email), Jui-Ling Yu - (email)

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82

On the first positive Neumann eigenvalue

Discrete and Continuous Dynamical Systems  Volume 17, Issue 1, Pages : 1 - 19, 2006

Wei-Ming Ni - (email), Xuefeng Wang - (email)

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83

Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy

Discrete and Continuous Dynamical Systems  Volume 15, Issue 4, Pages : 1035 - 1047, 2006

Denis Danilov - (email), Britta Nestler - (email)

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Global stability of traveling curved fronts in the Allen-Cahn equations

Discrete and Continuous Dynamical Systems  Volume 15, Issue 3, Pages : 819 - 832, 2006

Hirokazu Ninomiya - (email), Masaharu Taniguchi - (email)

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A Metapopulation Model Of Granuloma Formation In The Lung During Infection With Mycobacterium Tuberculosis

Mathematical Biosciences and Engineering  Volume 2, Issue 3, Pages : 535 - 560, 2005

Suman Ganguli - (email), David Gammack - (email), Denise E. Kirschner - (email)

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Structure of a class of traveling waves in delayed cellular neural networks

Discrete and Continuous Dynamical Systems  Volume 13, Issue 2, Pages : 339 - 359, 2005

Cheng-Hsiung Hsu - (email), Suh-Yuh Yang - (email)

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Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 653 - 662, 2004

Zhijun Liu - (email), Weidong Wang - (email)

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A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium

Discrete and Continuous Dynamical Systems  Volume 10, Issue 4, Pages : 925 - 940, 2004

Jonathan E. Rubin - (email)

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Biological computing with diffusion and excitable calcium stores

Mathematical Biosciences and Engineering  Volume 1, Issue 1, Pages : 147 - 159, 2004

H. G. E. Hentschel - (email), Alan Fine - (email), C. S. Pencea - (email)

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Travelling waves for solid-gas reaction-diffusion systems

DCDS Supplements  Volume 2003, Issue Special, Pages : 872 - 879, 2003

C. van der Mee - (email), Stella Vernier Piro - (email)

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Traveling waves for a diffusive Lotka-Volterra competition model I: singular perturbations

Discrete and Continuous Dynamical Systems - Series B  Volume 3, Issue 1, Pages : 79 - 95, 2002

Yuzo Hosono - (email)

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Existence of semi-discrete shocks

Discrete and Continuous Dynamical Systems  Volume 8, Issue 1, Pages : 163 - 190, 2001

Sylvie Benzoni-Gavage - (email), Pierre Huot - (email)

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