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<p>This paper studies the spatial dynamics in a diffusive model with herd behavior transition of prey and schooling behavior of predators. The existence and the local stability of the equilibria are explored. Turing instability is also studied and visually shown. By the normal forms related to codimension-two Turing-Hopf bifurcation, the spatial dynamics of the model near a Turing-Hopf bifurcation point are identified and classified. Numerical illustrations are shown to explain our analysis and complex spatiotemporal dynamics are observed. Furthermore, we found that the herd threshold not only stabilizes the system, but also induces periodic oscillations and Turing instability.</p>

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Turing-Hopf bifurcation in a diffusive predator-prey model with schooling and transitional herd behavior

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Yonghui Xia,
  • Jianglong Xiao,
  • Tonghua Zhang,
  • Lan Zou

摘要

This paper studies the spatial dynamics in a diffusive model with herd behavior transition of prey and schooling behavior of predators. The existence and the local stability of the equilibria are explored. Turing instability is also studied and visually shown. By the normal forms related to codimension-two Turing-Hopf bifurcation, the spatial dynamics of the model near a Turing-Hopf bifurcation point are identified and classified. Numerical illustrations are shown to explain our analysis and complex spatiotemporal dynamics are observed. Furthermore, we found that the herd threshold not only stabilizes the system, but also induces periodic oscillations and Turing instability.