Stability and spatiotemporal dynamics in a diffusive predator–prey model with nonlocal prey competition and nonlocal fear effect

Yanfei Du and Mengting Sui

Chaos, Solitons & Fractals, 2024, vol. 188, issue C

Abstract: In this paper, the stability and dynamics of a diffusive predator–prey model with nonlocal prey competition and nonlocal fear effect are investigated. Using the linear stability analysis, the possible bifurcation curves are obtained, and their positional relationship is determined by the discussion of their properties. The stability region for the positive equilibrium is obtained, whose boundary may consist of Turing bifurcation curves and mode-0 or mode-1 Hopf bifurcation curve. Thus, double Hopf bifurcation and Turing–Hopf bifurcation with different modes may occur. To explore the complex dynamics near the bifurcation points, the normal forms of double Hopf bifurcation and Turing–Hopf bifurcation with different modes for nonlocal model are derived. The stable spatially homogeneous or inhomogeneous periodic solutions, the stable spatially inhomogeneous quasi-periodic solution, and the coexistence of two stable spatially inhomogeneous periodic solutions or steady states are found.

Keywords: Normal form; Nonlocal fear effect; Nonlocal prey competition; Double Hopf bifurcation; Turing–Hopf bifurcation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s096007792401049x

DOI: 10.1016/j.chaos.2024.115497

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