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<p>This paper examines the dynamics of a predator–prey system with Allee effect and analyzes how the cross-diffusion causes Turing instability of its spatially homogeneous periodic solutions. Firstly, we show the existence of Hopf bifurcating periodic solutions of the ordinary differential system. Secondly, we discuss the effect of cross-diffusion on the stability of the positive equilibrium. We further prove the existence of periodic solutions for the perturbed auxiliary equations. Finally, by using Floquet theory we give Turing instability of Hopf bifurcating periodic solutions for the cross-diffusion predator–prey system.</p>

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Turing instability of the periodic solutions for a predator–prey model with Allee effect and cross-diffusion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月19日

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  • Hong Yang,
  • Zhaoman Zhong

摘要

This paper examines the dynamics of a predator–prey system with Allee effect and analyzes how the cross-diffusion causes Turing instability of its spatially homogeneous periodic solutions. Firstly, we show the existence of Hopf bifurcating periodic solutions of the ordinary differential system. Secondly, we discuss the effect of cross-diffusion on the stability of the positive equilibrium. We further prove the existence of periodic solutions for the perturbed auxiliary equations. Finally, by using Floquet theory we give Turing instability of Hopf bifurcating periodic solutions for the cross-diffusion predator–prey system.