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Bifurcation analysis of a diffusive predator–prey system with nonconstant death rate and Holling III functional response

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  • Yang, Ruizhi
  • Wei, Junjie

Abstract

In this paper, a diffusive predator–prey system with Holling III functional response and nonconstant death rate subject to Neumann boundary condition is considered. We study the stability of equilibria, and Turing instability of the positive equilibrium. We also perform a detailed Hopf bifurcation analysis to PDE system, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution. In addition, some numerical simulations are carried out.

Suggested Citation

  • Yang, Ruizhi & Wei, Junjie, 2015. "Bifurcation analysis of a diffusive predator–prey system with nonconstant death rate and Holling III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 1-13.
    • Handle: RePEc:eee:chsofr:v:70:y:2015:i:c:p:1-13
    DOI: 10.1016/j.chaos.2014.10.011
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    References listed on IDEAS

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    1. Wijeratne, A.W. & Yi, Fengqi & Wei, Junjie, 2009. "Bifurcation analysis in the diffusive Lotka–Volterra system: An application to market economy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 902-911.
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    Cited by:

    1. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.

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