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<p>In a two-dimensional space, we investigate a spatiotemporally discrete predator-prey model based on coupled map lattice, with diffusion and advection being its core characteristics. By considering diffusion and advection, we explore and derive the conditions for the occurrence of pure Turing instability, Neimark-Sacker-Turing instability, and flip-Turing instability. These instabilities triggered the evolution of the system from bifurcation to chaos. Additionally, we analyze the dynamical behavior of the model under spatially homogeneous steady-state conditions, including stability analysis, codimension-1 bifurcations, and codimension-2 bifurcations. Through numerical simulations, we verify the obtained results and use the maximum Lyapunov exponent to characterize the transition from bifurcation to chaos. The complex spatiotemporal dynamic behaviors exhibited by the system are of great significance for our deeper understanding of ecosystems and for their effective management.</p>

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Dynamical analysis of a discrete reaction-diffusion-convection predator-prey model based on coupled map lattices

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Xiongxiong Du,
  • Xiaoling Han

摘要

In a two-dimensional space, we investigate a spatiotemporally discrete predator-prey model based on coupled map lattice, with diffusion and advection being its core characteristics. By considering diffusion and advection, we explore and derive the conditions for the occurrence of pure Turing instability, Neimark-Sacker-Turing instability, and flip-Turing instability. These instabilities triggered the evolution of the system from bifurcation to chaos. Additionally, we analyze the dynamical behavior of the model under spatially homogeneous steady-state conditions, including stability analysis, codimension-1 bifurcations, and codimension-2 bifurcations. Through numerical simulations, we verify the obtained results and use the maximum Lyapunov exponent to characterize the transition from bifurcation to chaos. The complex spatiotemporal dynamic behaviors exhibited by the system are of great significance for our deeper understanding of ecosystems and for their effective management.