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Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response

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  • Han, Renji
  • Dai, Binxiang

Abstract

A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.

Suggested Citation

  • Han, Renji & Dai, Binxiang, 2017. "Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 90-109.
    • Handle: RePEc:eee:chsofr:v:96:y:2017:i:c:p:90-109
    DOI: 10.1016/j.chaos.2016.12.022
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    References listed on IDEAS

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    1. Li, Wan-Tong & Yan, Xiang-Ping & Zhang, Cun-Hua, 2008. "Stability and Hopf bifurcation for a delayed cooperation diffusion system with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 227-237.
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    Cited by:

    1. Ma, Zhan-Ping & Yue, Jia-Long, 2023. "Cross diffusion induced spatially inhomogeneous Hopf bifurcation for a three species Lotka–Volterra food web model with cycle," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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