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

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  • Du, Yanfei
  • Sui, Mengting

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.

Suggested Citation

  • Du, Yanfei & Sui, Mengting, 2024. "Stability and spatiotemporal dynamics in a diffusive predator–prey model with nonlocal prey competition and nonlocal fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s096007792401049x
    DOI: 10.1016/j.chaos.2024.115497
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