Bifurcation analysis of a diffusive predator–prey system with nonmonotonic functional response

被引：0
作者：
Bounsanong Sounvoravong
Jianping Gao
Shangjiang Guo
机构：
[1] Hunan University,College of Mathematics and Econometrics
来源：
Nonlinear Dynamics | 2018年 / 94卷
关键词：
Diffusion; Kinetic system; Hopf bifurcation; Steady-state bifurcation; 35J20; 35J60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a diffusive predator–prey model with nonmonotonic functional response is investigated. The stability of the positive spatially homogeneous steady states and bifurcations of spatially homogeneous/nonhomogeneous time-periodic solutions as well as steady-state solutions are studied. In particular, the formulas determining the direction and the stability of the bifurcating periodic solutions are obtained. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulations.
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页码：2901 / 2918
页数：17
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共 61 条
  • [1] Chen S(2016)Dynamics of a diffusive predator–prey system with a nonlinear growth rate for the predator J. Differ. Equ. 260 7923-7939
  • [2] Jianshe Y(2006)A diffusive predator-prey model with a protection zone J. Differ. Equ. 229 63-91
  • [3] Du Y(2001)Stability and bifurcation for a delayed predator–prey model and the effect of diffusion J. Math. Anal. Appl. 254 433-463
  • [4] Shi J(2018)Patterns in a nonlocal time-delayed reaction–diffusion equation Zeitschrift für angewandte Mathematik und Physik 69 1-31
  • [5] Faria T(2016)Generalized Hopf bifurcation for neutral functional differential equations Int. J. Bifurc. Chaos 26 1650231-1448
  • [6] Guo S(2015)Stability and bifurcation in a reaction–diffusion model with nonlocal delay effect J. Differ. Equ. 259 1409-3529
  • [7] Guo S(2013)Patterns in hierarchical networks of neuronal oscillators with J. Differ. Equ. 254 3501-817
  • [8] Guo S(2016) symmetry J. Differ. Equ. 260 781-1852
  • [9] Guo S(2009)Hopf bifurcation in a diffusive Lotka–Volterra type system with nonlocal delay effect Math. Models Methods Appl. Sci. 19 1797-398
  • [10] Man J(1959)Pattern formation in a ring network with delay Can. Entomol. 91 385-134
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