Turing Patterns of a Lotka-Volterra Competitive System with Nonlocal Delay

This paper focuses on the dynamical behavior of a Lotka–Volterra competitive system with nonlocal delay. We first establish the conditions of Turing bifurcation occurring in the system. According t...

[1]  Jianshe Yu,et al.  Dynamics of a diffusive predator–prey system with a nonlinear growth rate for the predator , 2016 .

[2]  Jianshe Yu,et al.  Stability and bifurcation on predator-prey systems with nonlocal prey competition , 2017 .

[3]  Yongli Song,et al.  Cross-diffusion induced spatiotemporal patterns in a predator–prey model with herd behavior , 2015 .

[4]  S. A. Gourley.  Travelling front solutions of a nonlocal Fisher equation , 2000, Journal of mathematical biology.

[5]  G. Raoul,et al.  Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait , 2012 .

[6]  Jian Xu,et al.  Analysis of spatiotemporal patterns in a single species reaction–diffusion model with spatiotemporal delay , 2015 .

[7]  Jian Xu,et al.  Pattern dynamics of a predator–prey reaction–diffusion model with spatiotemporal delay , 2015 .

[8]  Shangjiang Guo,et al.  Bifurcation Phenomena in a Lotka-Volterra Model with Cross-Diffusion and Delay Effect , 2017, Int. J. Bifurc. Chaos.

[9]  Wan-Tong Li,et al.  Multiple bifurcations in a delayed predator–prey diffusion system with a functional response , 2010 .

[10]  Chunhua Ou,et al.  Traveling Wavefronts in a Delayed Food-limited Population Model , 2007, SIAM J. Math. Anal..

[11]  Shigui Ruan,et al.  Convergence and Travelling Fronts in Functional Differential Equations with Nonlocal Terms: A Competition Model , 2003, SIAM J. Math. Anal..

[12]  Wan-Tong Li,et al.  Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems , 2006 .

[13]  Shangjiang Guo,et al.  Patterns in a nonlocal time-delayed reaction–diffusion equation , 2018 .

[14]  J. So,et al.  Dynamics of a food-limited population model incorporating nonlocal delays on a finite domain , 2002, Journal of mathematical biology.

[15]  B. Perthame,et al.  Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation , 2010, 1011.4561.

[16]  Yongli Song,et al.  Hopf bifurcation in a reaction–diffusion equation with distributed delay and Dirichlet boundary condition , 2017 .

[17]  Shangjiang Guo,et al.  Spatio-temporal patterns in a diffusive model with non-local delay effect , 2017 .

[18]  Nicholas F. Britton,et al.  Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model , 1990 .

[19]  Shigui Ruan,et al.  Turing instability and travelling waves in diffusive plankton models with delayed nutrient recycling , 1998 .

[20]  Wan-Tong Li,et al.  Bistable wavefronts in a diffusive and competitive Lotka-Volterra type system with nonlocal delays , 2008 .

[21]  Junjie Wei,et al.  Spatiotemporal pattern formation and multiple bifurcations in a diffusive bimolecular model , 2010 .

[22]  Zhi-Cheng Wang,et al.  Traveling wave solutions in a nonlocal reaction-diffusion population model , 2016 .

[23]  Xiang-Ping Yan,et al.  Direction of Hopf bifurcation in a delayed Lotka–Volterra competition diffusion system , 2009 .

[24]  Wenjie Zuo,et al.  Stability and bifurcation analysis of a reaction–diffusion equation with spatio-temporal delay , 2015 .

[25]  Stephen A. Gourley,et al.  A predator-prey reaction-diffusion system with nonlocal effects , 1996 .

[26]  Shigui Ruan,et al.  Spatial, temporal and spatiotemporal patterns of diffusive predator-prey models with mutual interference , 2015 .

[27]  S. Roy Choudhury.  Turing Instability in Competition Models with Delay I: Linear Theory , 1994, SIAM J. Appl. Math..

[28]  Prashanta Kumar Mandal,et al.  Spatiotemporal dynamics of reaction–diffusion models of interacting populations , 2014 .

[29]  Jong-Shenq Guo,et al.  Recent developments on wave propagation in 2-species competition systems , 2012 .

[30]  Li Li,et al.  Pattern dynamics of a spatial predator–prey model with noise , 2012 .

[31]  Xiao-Qiang Zhao,et al.  Monotone wavefronts of the nonlocal Fisher–KPP equation , 2011 .

[32]  Ying-Hui Yang,et al.  On a predator-prey reaction-diffusion model with nonlocal effects , 2017, Commun. Nonlinear Sci. Numer. Simul..

[33]  Shangbing Ai,et al.  Traveling wave fronts for generalized Fisher equations with spatio-temporal delays , 2007 .

[34]  Henri Berestycki,et al.  The non-local Fisher–KPP equation: travelling waves and steady states , 2009 .

[35]  Rui Peng,et al.  Spatiotemporal patterns in a reaction–diffusion model with the Degn–Harrison reaction scheme☆ , 2013 .

[36]  Teresa Faria,et al.  Normal forms and Hopf bifurcation for partial differential equations with delays , 2000 .

[37]  N. Britton.  Aggregation and the competitive exclusion principle. , 1989, Journal of Theoretical Biology.

[38]  Zhaosheng Feng,et al.  Traveling waves for the nonlocal diffusive single species model with Allee effect , 2016 .

[39]  Lenya Ryzhik,et al.  On the nonlocal Fisher–KPP equation: steady states, spreading speed and global bounds , 2013, 1307.3001.

[40]  Matthieu Alfaro,et al.  Bistable travelling waves for nonlocal reaction diffusion equations , 2013, 1303.3554.

[41]  Shangjiang Guo,et al.  Hopf bifurcation in a diffusive Lotka–Volterra type system with nonlocal delay effect , 2016 .

[42]  Junjie Wei,et al.  Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩ , 2009 .

[43]  Jianhong Wu,et al.  Monotone traveling waves for delayed Lotka-Volterra competition systems , 2012 .