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

Reeta Yadav and Moitri Sen

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 283-302

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.

Keywords: Global stability; Persistence of solution; Steady-state bifurcation; Hopf-bifurcation; Turing instability; Constant and non-constant steady state (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:283-302

DOI: 10.1016/j.matcom.2024.05.019

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