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Spatio-temporal complexity in a prey-predator system with Holling type-IV response and Leslie-type numerical response: Turing and steady-state bifurcations

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  • Yadav, Reeta
  • Sen, Moitri

Abstract

In this study, we unravel the intricate dynamics of a spatio-temporal prey-predator model featuring a Holling type-IV functional response and Leslie-type predator numerical response under Neumann boundary conditions. Our analysis encompasses the uniform persistence and global asymptotic stability of a positive equilibrium, validated by precise numerical simulations. Additionally, we explore Turing instability and spatial pattern emergence through linear stability analysis. Our primary emphasis lies in the realm of spatio-temporal bifurcation analysis, through which we establish criteria for the presence or absence of non-constant steady states within n-dimensional diffusion models. Moreover, we discern precise conditions governing Hopf bifurcation and steady-state bifurcation in 1-dimensional diffusion models. These findings offer theoretical insights that align with the intricate dynamic patterns observed in our numerical simulations.

Suggested Citation

  • Yadav, Reeta & Sen, Moitri, 2024. "Spatio-temporal complexity in a prey-predator system with Holling type-IV response and Leslie-type numerical response: Turing and steady-state bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 283-302.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:283-302
    DOI: 10.1016/j.matcom.2024.05.019
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    References listed on IDEAS

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    1. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
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