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Diffusion-Induced Instability of the Periodic Solutions in a Reaction-Diffusion Predator-Prey Model with Dormancy of Predators

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  • Mi Wang

    (College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China
    College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China)

Abstract

A reaction-diffusion predator-prey model with the dormancy of predators is considered in this paper. We are concerned with the long-time behaviors of the solutions of this system. We divided our investigations into two cases: for the ODEs system, we study the existence and stability of the equilibrium solutions and derive precise conditions on system parameters so that the system can undergo Hopf bifurcations around the positive equilibrium solution. Moreover, the properties of Hopf bifurcation are studied in detail. For the reaction-diffusion system, we are able to derive conditions on the diffusion coefficients so that the spatially homogeneous Hopf bifurcating periodic solutions can undergo diffusion-triggered instability. To support our theoretical analysis, we also include several numerical results.

Suggested Citation

  • Mi Wang, 2023. "Diffusion-Induced Instability of the Periodic Solutions in a Reaction-Diffusion Predator-Prey Model with Dormancy of Predators," Mathematics, MDPI, vol. 11(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1875-:d:1124174
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    Cited by:

    1. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review," Sustainability, MDPI, vol. 15(16), pages 1-23, August.

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