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<p>In this paper, we study the impact of memory delay and distributed delay on the dynamics of a diffusive predator-prey model with predator-taxis. For the scenario without memory delay, our findings reveal that the distributed delay can lead to Turing bifurcation for the negative diffusion coefficient and lead to Hopf bifurcation for the positive diffusion coefficient. Furthermore, for fixed diffusion coefficient and distributed delay, the existence of memory delay can induce Hopf bifurcation thereby the spatially periodic solutions are generated. Also the combinations of memory delay and distributed delay can induce rich dynamic behaviors via Turing-Hopf bifurcation. Finally, we apply our theoretical findings to a predator-prey model with Holling type-I functional response to explain the emergence of various spatiotemporal patterns.</p>

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Spatiotemporal dynamics in a diffusive predator-prey model with spatial memory and distributed delay

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Yan Li,
  • Jianing Sun

摘要

In this paper, we study the impact of memory delay and distributed delay on the dynamics of a diffusive predator-prey model with predator-taxis. For the scenario without memory delay, our findings reveal that the distributed delay can lead to Turing bifurcation for the negative diffusion coefficient and lead to Hopf bifurcation for the positive diffusion coefficient. Furthermore, for fixed diffusion coefficient and distributed delay, the existence of memory delay can induce Hopf bifurcation thereby the spatially periodic solutions are generated. Also the combinations of memory delay and distributed delay can induce rich dynamic behaviors via Turing-Hopf bifurcation. Finally, we apply our theoretical findings to a predator-prey model with Holling type-I functional response to explain the emergence of various spatiotemporal patterns.