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

• Published in: Chaos, solitons and fractals solitons and fractals, 2024-11, Vol.188, p.115497, Article 115497
• Main Authors: Du, Yanfei, Sui, Mengting
• Format: Article
• Language: English
• Subjects: Double Hopf bifurcation; Nonlocal fear effect; Nonlocal prey competition; Normal form; Turing–Hopf bifurcation
• ISSN: 0960-0779
• DOI: 10.1016/j.chaos.2024.115497

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. •A model with nonlocal prey competition and nonlocal fear effect is investigated.•Hopf bifurcation of the nonlocal model can be spatially homogeneous or inhomogeneous.•The stability region for the positive equilibrium of nonlocal model is obtained.•Double Hopf and Turing–Hopf (TH) bifurcation of different modes are investigated.•The (0,n2)-mode (n2≠0) normal form of TH bifurcation for nonlocal system is derived.