Turing–Hopf bifurcation analysis of a predator–prey model with herd behavior and cross-diffusion

被引：0
作者：
Xiaosong Tang
Yongli Song
Tonghua Zhang
机构：
[1] Tongji University,Department of Mathematics
[2] Jinggangshan University,College of Mathematics and Physics
[3] Swinburne University of Technology,Department of Mathematics
来源：
Nonlinear Dynamics | 2016年 / 86卷
关键词：
Predator–prey model; Herd behavior; Cross-diffusion; Turing–Hopf bifurcation; Spatially inhomogeneous periodic solution;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider a predator–prey model with herd behavior and cross-diffusion subject to homogeneous Neumann boundary condition. Firstly, the existence and priori bound of a solution for the model without cross-diffusion are shown. Then, by computing and analyzing the normal form on the center manifold associated with the Turing–Hopf bifurcation, we find a wealth of spatiotemporal dynamics near the Turing–Hopf bifurcation point under suitable conditions. Furthermore, some numerical simulations to illustrate the theoretical analysis are carried out.
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页码：73 / 89
页数：16
相关论文
共 149 条
  • [1] Volterra V(1901)Sui tentutive di applicazione delle mathematiche alle seienze biologiche e sociali Ann. Radioelectr. Univ. Romandes 23 436-458
  • [2] Volterra V(1926)Variazione e fluttuazini del numero dindividui in specie animali conviventi Mem. R. Accad. Naz. dei Lincei 2 31-113
  • [3] Zhang T(2014)Delay-induced Turing instability in reaction–diffusion equations Phys. Rev. E 90 052908-277
  • [4] Zang H(2014)Spatio-temporal patterns in a predator–prey model with hyperbolic mortality Nonlinear Dyn. 78 265-70
  • [5] Zhang T(2014)Bifurcation analysis of a diffusive ratio-dependent predator–prey model Nonlinear Dyn. 78 49-12
  • [6] Xing Y(2016)Turing instability and pattern induced by cross-diffusion in a predator–prey system with Allee effect Appl. Math. Comput. 275 1-508
  • [7] Zang H(1986)Predator–prey systems with groups defence: the paradox of enrichment revisited Bull. Math. Biol. 48 493-723
  • [8] Han M(1968)A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates Biotechnol. Bioeng. 10 707-2338
  • [9] Song Y(2011)Modeling herd behavior in population systems Nonlinear Anal. RWA 12 2319-1843
  • [10] Zou X(2012)Predator–prey dynamics with square root functional responses Nonlinear Anal. RWA 13 1837-391
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