一个扩散模型中恐惧效应与集群行为协同诱导的时空动力学研究

Abstract

Abstract:

In this paper, we study the spatiotemporal dynamics in a diffusive predator-prey model with the homogeneous Neumann boundary condition. Our study indicates that the interaction between fear and schooling behavior induces very rich and interesting spatiotemporal dynamics. The conditions for Turing instability and Turing-Hopf bifurcation emerging are explored at length. By utilizing the normal form method, the spatiotemporal dynamics of the spatial model near the Turing-Hopf bifurcation point are classified. And rich numerical simulations are used to confirm the theoretical analysis. Finally, we summarize the great influence of the fear effect and schooling behavior. We found that the schooling behavior of prey cannot counteract high-level fear, while it offsets the low-level fear. Moreover, the fear effect induces Turing instability of the system with the schooling behavior. However, the fear effect neither changes the stability of coexistence equilibrium, nor induces periodic solutions or Turing instability of the system without the schooling behavior.

Key words: Turing-Hopf bifurcation, Turing instability, Schooling behavior, Fear effect, Dynamical classification, Predator-prey

CLC Number:

0175.23

Xiao Jianglong, Song Yongli, Xia Yonghui. Spatiotemporal Dynamics Induced by the Interaction Between Fear and Schooling Behavior in a Diffusive Model[J].Acta mathematica scientia,Series A, 2024, 44(6): 1577-1594.

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References 41

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Spatiotemporal Dynamics Induced by the Interaction Between Fear and Schooling Behavior in a Diffusive Model

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