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Analysis of optimal boundary control for a three-dimensional reaction-diffusion system

Numerical Algebra, Control and Optimization  Volume 7, Issue 3, Pages : 325 - 344, 2017

Wanli Yang - (email), Jie Sun - (email), Su Zhang - (email)

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2

Pattern dynamics of a delayed eco-epidemiological model with disease in the predator

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 5, Pages : 1025 - 1042, 2017

Jing Li - (email), Zhen Jin - (email), Gui-Quan Sun - (email), Li-Peng Song - (email)

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3

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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4

Bifurcations analysis of Leslie-Gower predator-prey models with nonlinear predator-harvesting

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 5, Pages : 1187 - 1206, 2017

Changrong Zhu - (email), Lei Kong - (email)

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5

Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion

Discrete and Continuous Dynamical Systems  Volume 37, Issue 10, Pages : 5433 - 5454, 2017

Hongmei Cheng - (email), Rong Yuan - (email)

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6

A PDE model of intraguild predation with cross-diffusion

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 5, Pages : 25 - 25, 2017

Robert Stephen Cantrell - (email), Xinru Cao - (email), King-Yeung Lam - (email), Tian Xiang - (email)

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7

Long-time behavior of state functions for climate energy balance model

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 5, Pages : 1887 - 1897, 2017

Nataliia V. Gorban - (email), Olha V. Khomenko - (email), Liliia S. Paliichuk - (email), Alla M. Tkachuk - (email)

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8

Regularity of global attractors for reaction-diffusion systems with no more than quadratic growth

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 5, Pages : 1899 - 1908, 2017

Oleksiy V. Kapustyan - (email), Pavlo O. Kasyanov - (email), José Valero - (email)

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A periodic and diffusive predator-prey model with disease in the prey

Discrete and Continuous Dynamical Systems - Series S  Volume 10, Issue 3, Pages : 445 - 461, 2017

Xiaoling Li - (email), Guangping Hu - (email), Zhaosheng Feng - (email), Dongliang Li - (email)

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10

Bifurcation and spatiotemporal patterns in a Bazykin predator-prey model with self and cross diffusion and Beddington-DeAngelis response

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 717 - 740, 2016

Eric Avila-Vales - (email), Gerardo García-Almeida - (email), Erika Rivero-Esquivel - (email)

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11

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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12

Effect of cross-diffusion in the diffusion prey-predator model with a protection zone

Discrete and Continuous Dynamical Systems  Volume 37, Issue 3, Pages : 1539 - 1558, 2016

Shanbing Li - (email), Jianhua Wu - (email)

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13

Stable patterns with jump discontinuity in systems with Turing instability and hysteresis

Discrete and Continuous Dynamical Systems  Volume 37, Issue 2, Pages : 757 - 800, 2016

Steffen Härting - (email), Anna Marciniak-Czochra - (email), Izumi Takagi - (email)

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14

Spatial degeneracy vs functional response

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 8, Pages : 2811 - 2837, 2016

Yu-Xia Wang - (email), Wan-Tong Li - (email)

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15

Some class of parabolic systems applied to image processing

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 6, Pages : 1671 - 1687, 2016

Lekbir Afraites - (email), Abdelghafour Atlas - (email), Fahd Karami - (email), Driss Meskine - (email)

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16

Renormalized solutions to a reaction-diffusion system applied to image denoising

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 6, Pages : 1839 - 1858, 2016

Qiang Liu - (email), Zhichang Guo - (email), Chunpeng Wang - (email)

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17

Hopf periodic orbits for a ratio--dependent predator--prey model with stage structure

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 6, Pages : 1859 - 1867, 2016

Jaume Llibre - (email), Claudio Vidal - (email)

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18

Bifurcation analysis of a diffusive plant-wrack model with tide effect on the wrack

Mathematical Biosciences and Engineering  Volume 13, Issue 4, Pages : 857 - 885, 2016

Jun Zhou - (email)

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19

Threshold asymptotic behaviors for a delayed nonlocal reaction-diffusion model of mistletoes and birds in a 2D strip

Communications on Pure and Applied Analysis  Volume 15, Issue 4, Pages : 1471 - 1495, 2016

Huimin Liang - (email), Peixuan Weng - (email), Yanling Tian - (email)

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20

Bogdanov-Takens bifurcation of codimension 3 in a predator-prey model with constant-yield predator harvesting

Communications on Pure and Applied Analysis  Volume 15, Issue 3, Pages : 1041 - 1055, 2016

Jicai Huang - (email), Sanhong Liu - (email), Shigui Ruan - (email), Xinan Zhang - (email)

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21

Pullback uniform dissipativity of stochastic reversible Schnackenberg equations

DCDS Supplements  Volume 2015, Issue special, Pages : 1134 - 1142, 2015

Yuncheng You - (email)

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22

Stability analysis of reaction-diffusion models on evolving domains: The effects of cross-diffusion

Discrete and Continuous Dynamical Systems  Volume 36, Issue 4, Pages : 2133 - 2170, 2015

Anotida Madzvamuse - (email), Hussaini Ndakwo - (email), Raquel Barreira - (email)

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23

Spatial dynamics of a diffusive predator-prey model with stage structure

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 6, Pages : 1831 - 1853, 2015

Liang Zhang - (email), Zhi-Cheng Wang - (email)

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24

Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy

Mathematical Biosciences and Engineering  Volume 12, Issue 5, Pages : 1065 - 1081, 2015

Qizhen Xiao - (email), Binxiang Dai - (email)

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25

Remarks on pattern formation in a model for hair follicle spacing

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 5, Pages : 1555 - 1572, 2015

Peter Rashkov - (email)

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Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology

Networks and Heterogeneous Media  Volume 10, Issue 2, Pages : 369 - 385, 2015

Bedr'Eddine Ainseba - (email), Mostafa Bendahmane - (email), Yuan He - (email)

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27

Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium

Networks and Heterogeneous Media  Volume 9, Issue 4, Pages : 669 - 682, 2014

Danielle Hilhorst - (email), Hideki Murakawa - (email)

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Homogenization of a thermo-diffusion system with Smoluchowski interactions

Networks and Heterogeneous Media  Volume 9, Issue 4, Pages : 739 - 762, 2014

Oleh Krehel - (email), Toyohiko Aiki - (email), Adrian Muntean - (email)

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29

Graph-theoretic approach to stability of multi-group models with dispersal

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 1, Pages : 259 - 280, 2014

Chunmei Zhang - (email), Wenxue Li - (email), Ke Wang - (email)

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30

Existence and multiplicity of segregated solutions to a cell-growth contact inhibition problem

Discrete and Continuous Dynamical Systems  Volume 35, Issue 4, Pages : 1479 - 1501, 2014

Gonzalo Galiano - (email), Sergey Shmarev - (email), Julian Velasco - (email)

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31

Avoidance behavior in intraguild predation communities: A cross-diffusion model

Discrete and Continuous Dynamical Systems  Volume 35, Issue 4, Pages : 1641 - 1663, 2014

Daniel Ryan - (email), Robert Stephen Cantrell - (email)

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32

Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 10, Pages : 3169 - 3189, 2014

Sze-Bi Hsu - (email), Junping Shi - (email), Feng-Bin Wang - (email)

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33

Spreading speeds and traveling wave solutions in a competitive reaction-diffusion model for species persistence in a stream

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 10, Pages : 3267 - 3281, 2014

Bingtuan Li - (email), William F. Fagan - (email), Garrett Otto - (email), Chunwei Wang - (email)

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34

Spatiotemporal complexity in a predator--prey model with weak Allee effects

Mathematical Biosciences and Engineering  Volume 11, Issue 6, Pages : 1247 - 1274, 2014

Yongli Cai - (email), Malay Banerjee - (email), Yun Kang - (email), Weiming Wang - (email)

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35

Asymptotic effects of boundary perturbations in excitable systems

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 7, Pages : 2039 - 2045, 2014

Monica De Angelis - (email), Pasquale Renno - (email)

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36

On global existence for the Gierer-Meinhardt system

Discrete and Continuous Dynamical Systems  Volume 35, Issue 1, Pages : 583 - 591, 2014

Henghui Zou - (email)

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37

Regular solutions and global attractors for reaction-diffusion systems without uniqueness

Communications on Pure and Applied Analysis  Volume 13, Issue 5, Pages : 1891 - 1906, 2014

Oleksiy V. Kapustyan - (email), Pavlo O. Kasyanov - (email), José Valero - (email)

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38

Multiple positive periodic solutions to a predator-prey model with Leslie-Gower Holling-type II functional response and harvesting terms

Discrete and Continuous Dynamical Systems - Series S  Volume 7, Issue 6, Pages : 1203 - 1214, 2014

Zengji Du - (email), Xiao Chen - (email), Zhaosheng Feng - (email)

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39

On a diffusive predator-prey model with nonlinear harvesting

Mathematical Biosciences and Engineering  Volume 11, Issue 4, Pages : 807 - 821, 2014

Peng Feng - (email)

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40

Positive steady states for a prey-predator cross-diffusion system with a protection zone and Holling type II functional response

DCDS Supplements  Volume 2013, Issue special, Pages : 597 - 603, 2013

Kazuhiro Oeda - (email)

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41

Bifurcation analysis in a predator-prey model with constant-yield predator harvesting

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 8, Pages : 2101 - 2121, 2013

Jicai Huang - (email), Yijun Gong - (email), Shigui Ruan - (email)

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42

Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks

Mathematical Biosciences and Engineering  Volume 10, Issue 4, Pages : 1207 - 1226, 2013

Maya Mincheva - (email), Gheorghe Craciun - (email)

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43

Finite element approximation of a population spatial adaptation model

Mathematical Biosciences and Engineering  Volume 10, Issue 3, Pages : 637 - 647, 2013

Gonzalo Galiano - (email), Julián Velasco - (email)

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44

Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction

Discrete and Continuous Dynamical Systems  Volume 33, Issue 9, Pages : 4041 - 4069, 2013

Sheng-Chen Fu - (email), Je-Chiang Tsai - (email)

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45

Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey

Mathematical Biosciences and Engineering  Volume 10, Issue 2, Pages : 345 - 367, 2013

Eduardo González-Olivares - (email), Betsabé González-Yañez - (email), Jaime Mena-Lorca - (email), José D. Flores - (email)

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46

A link between microscopic and macroscopic models of self-organized aggregation

Networks and Heterogeneous Media  Volume 7, Issue 4, Pages : 705 - 740, 2012

Tadahisa Funaki - (email), Hirofumi Izuhara - (email), Masayasu Mimura - (email), Chiyori Urabe - (email)

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47

On limit systems for some population models with cross-diffusion

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 8, Pages : 2745 - 2769, 2012

Kousuke Kuto - (email), Yoshio Yamada - (email)

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48

On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 6, Pages : 1639 - 1649, 2012

Matthieu Alfaro - (email), Hiroshi Matano - (email)

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49

Stabilization of a reaction-diffusion system modelling malaria transmission

Discrete and Continuous Dynamical Systems - Series B  Volume 17, Issue 6, Pages : 1673 - 1684, 2012

Sebastian Aniţa - (email), Vincenzo Capasso - (email)

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50

Preconditioning operators and $L^\infty$ attractor for a class of reaction-diffusion systems

Communications on Pure and Applied Analysis  Volume 11, Issue 6, Pages : 2179 - 2199, 2012

Boris Andreianov - (email), Halima Labani - (email)

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51

On a phase field model for solid-liquid phase transitions

Discrete and Continuous Dynamical Systems  Volume 32, Issue 6, Pages : 1997 - 2025, 2012

Sylvie Benzoni-Gavage - (email), Laurent Chupin - (email), Didier Jamet - (email), Julien Vovelle - (email)

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52

Traveling curved fronts in monotone bistable systems

Discrete and Continuous Dynamical Systems  Volume 32, Issue 6, Pages : 2339 - 2374, 2012

Zhi-Cheng Wang - (email)

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53

Existence of traveling waves with transition layers for some degenerate cross-diffusion systems

Communications on Pure and Applied Analysis  Volume 11, Issue 3, Pages : 911 - 934, 2011

Yanxia Wu - (email), Yaping Wu - (email)

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54

Standing waves in a complex Ginzburg-Landau equation with time-delay feedback

DCDS Supplements  Volume 2011, Issue Special, Pages : 1329 - 1334, 2011

Michael Stich - (email), Carsten Beta - (email)

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55

The singular limit of a haptotaxis model with bistable growth

Communications on Pure and Applied Analysis  Volume 11, Issue 1, Pages : 209 - 228, 2011

Elisabeth Logak - (email), Chao Wang - (email)

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56

Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction

Discrete and Continuous Dynamical Systems - Series B  Volume 16, Issue 1, Pages : 189 - 196, 2011

Sheng-Chen Fu - (email)

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57

Hopf dances near the tips of Busse balloons

Discrete and Continuous Dynamical Systems - Series S  Volume 5, Issue 1, Pages : 61 - 92, 2011

Arjen Doelman - (email), Jens D. M. Rademacher - (email), Sjors van der Stelt - (email)

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58

A relation between cross-diffusion and reaction-diffusion

Discrete and Continuous Dynamical Systems - Series S  Volume 5, Issue 1, Pages : 147 - 158, 2011

Hideki Murakawa - (email)

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59

Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains

Discrete and Continuous Dynamical Systems - Series S  Volume 4, Issue 1, Pages : 67 - 82, 2010

Arnaud Ducrot - (email), Vincent Guyonne - (email), Michel Langlais - (email)

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60

Analysis of a predator-prey model with predators impulsively diffusing between two patches

Discrete and Continuous Dynamical Systems - Series B  Volume 14, Issue 3, Pages : 1081 - 1094, 2010

Jianjun Jiao - (email), Lansun Chen - (email)

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61

Stationary patterns for an adsorbate-induced phase transition model I: Existence

Discrete and Continuous Dynamical Systems - Series B  Volume 14, Issue 3, Pages : 1105 - 1117, 2010

Kousuke Kuto - (email), Tohru Tsujikawa - (email)

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62

Morphological spatial patterns in a reaction diffusion model for metal growth

Mathematical Biosciences and Engineering  Volume 7, Issue 2, Pages : 237 - 258, 2010

Benedetto Bozzini - (email), Deborah Lacitignola - (email), Ivonne Sgura - (email)

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63

Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains

Discrete and Continuous Dynamical Systems - Series B  Volume 11, Issue 4, Pages : 805 - 822, 2009

Sebastian Aniţa - (email), William Edward Fitzgibbon - (email), Michel Langlais - (email)

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Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease

Discrete and Continuous Dynamical Systems - Series B  Volume 11, Issue 4, Pages : 823 - 853, 2009

Mostafa Bendahmane - (email), Mauricio Sepúlveda - (email)

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65

Relaxation oscillation profile of limit cycle in predator-prey system

Discrete and Continuous Dynamical Systems - Series B  Volume 11, Issue 4, Pages : 893 - 911, 2009

Sze-Bi Hsu - (email), Junping Shi - (email)

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The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness

Discrete and Continuous Dynamical Systems - Series S  Volume 2, Issue 1, Pages : 55 - 66, 2009

Alexey Cheskidov - (email), Songsong Lu - (email)

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67

Spreading speeds for a partially cooperative 2-species reaction-diffusion model

Discrete and Continuous Dynamical Systems  Volume 23, Issue 3, Pages : 1087 - 1098, 2008

Hans F. Weinberger - (email), Kohkichi Kawasaki - (email), Nanako Shigesada - (email)

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68

Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis

Networks and Heterogeneous Media  Volume 3, Issue 4, Pages : 863 - 879, 2008

Mostafa Bendahmane - (email)

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69

Global exponential stability of traveling waves in monotone bistable systems

Discrete and Continuous Dynamical Systems  Volume 21, Issue 2, Pages : 601 - 623, 2008

Je-Chiang Tsai - (email)

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70

"Traveling wave'' solutions of Fitzhugh model with cross-diffusion

Mathematical Biosciences and Engineering  Volume 5, Issue 2, Pages : 239 - 260, 2008

F. Berezovskaya - (email), Erika Camacho - (email), Stephen Wirkus - (email), Georgy Karev - (email)

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71

Relative compactness in $L^p$ of solutions of some 2m components competition-diffusion systems

Discrete and Continuous Dynamical Systems  Volume 21, Issue 1, Pages : 233 - 244, 2008

Danielle Hilhorst - (email), Masato Iida - (email), Masayasu Mimura - (email), Hirokazu Ninomiya - (email)

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72

Modelling of wettability alteration processes in carbonate oil reservoirs

Networks and Heterogeneous Media  Volume 3, Issue 1, Pages : 149 - 183, 2008

Liping Yu - (email), Hans Kleppe - (email), Terje Kaarstad - (email), Svein M. Skjaeveland - (email), Steinar Evje - (email), Ingebret Fjelde - (email)

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73

Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony

Communications on Pure and Applied Analysis  Volume 6, Issue 4, Pages : 1145 - 1165, 2007

Peng Feng - (email), Zhengfang Zhou - (email)

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Interaction of diffusion and delay

Discrete and Continuous Dynamical Systems - Series B  Volume 8, Issue 1, Pages : 95 - 105, 2007

Karl Peter Hadeler - (email), Shigui Ruan - (email)

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Periodic solutions in a delayed predator-prey models with nonmonotonic functional response

Discrete and Continuous Dynamical Systems - Series B  Volume 8, Issue 1, Pages : 175 - 185, 2007

Wan-Tong Li - (email), Yong-Hong Fan - (email)

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Alternative models for cyclic lemming dynamics

Mathematical Biosciences and Engineering  Volume 4, Issue 1, Pages : 85 - 99, 2006

Hao Wang - (email), Yang Kuang - (email)

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On the dynamics of a ratio dependent Predator-Prey system with diffusion and delay

Discrete and Continuous Dynamical Systems - Series B  Volume 6, Issue 6, Pages : 1321 - 1338, 2006

Marcos Lizana - (email), Julio Marín - (email)

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78

Periodic solutions for a 3x 3 competitive system with cross-diffusion

Discrete and Continuous Dynamical Systems  Volume 15, Issue 3, Pages : 725 - 746, 2006

Salomé Martínez - (email), Wei-Ming Ni - (email)

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79

Global existence of solutions of an activator-inhibitor system

Discrete and Continuous Dynamical Systems  Volume 14, Issue 4, Pages : 737 - 751, 2006

Huiqiang Jiang - (email)

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80

Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue

Networks and Heterogeneous Media  Volume 1, Issue 1, Pages : 185 - 218, 2006

Mostafa Bendahmane - (email), Kenneth H. Karlsen - (email)

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Coexistence states for a prey-predator model with cross-diffusion

DCDS Supplements  Volume 2005, Issue Special, Pages : 536 - 545, 2005

Kousuke Kuto - (email), Yoshio Yamada - (email)

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82

Global existence of solutions to a cross-diffusion system in higher dimensional domains

Discrete and Continuous Dynamical Systems  Volume 12, Issue 2, Pages : 185 - 192, 2004

Yi Li - (email), Chunshan Zhao - (email)

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Stoichiometric Plant-Herbivore Models and Their Interpretation

Mathematical Biosciences and Engineering  Volume 1, Issue 2, Pages : 215 - 222, 2004

Yang Kuang - (email), Jef Huisman - (email), James J. Elser - (email)

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The impact of state feedback control on a predator-prey model with functional response

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 607 - 614, 2004

Haiying Jing - (email), Zhaoyu Yang - (email)

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Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 705 - 711, 2004

H. Malchow - (email), F.M. Hilker - (email), S.V. Petrovskii - (email)

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86

The effect of local prevention in an SIS model with diffusion

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 739 - 746, 2004

Toru Sasaki - (email)

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Turing instabilities and pattern formation in a benthic nutrient-microorganism system

Mathematical Biosciences and Engineering  Volume 1, Issue 1, Pages : 111 - 130, 2004

Martin Baurmann - (email), Wolfgang Ebenhöh - (email), Ulrike Feudel - (email)

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88

On a unilateral reaction-diffusion system and a nonlocal evolution obstacle problem

Communications on Pure and Applied Analysis  Volume 3, Issue 1, Pages : 85 - 95, 2004

José-Francisco Rodrigues - (email), João Lita da Silva - (email)

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89

Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion

Discrete and Continuous Dynamical Systems  Volume 10, Issue 3, Pages : 719 - 730, 2004

Y. S. Choi - (email), Roger Lui - (email), Yoshio Yamada - (email)

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On a limiting system in the Lotka--Volterra competition with cross-diffusion

Discrete and Continuous Dynamical Systems  Volume 10, Issue 1/2, Pages : 435 - 458, 2003

Yuan Lou - (email), Wei-Ming Ni - (email), Shoji Yotsutani - (email)

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