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<p>This work is devoted to the asymptotic spreading speed of predator populations and the existence/nonexistence of forced waves in a stage-structured predator–prey model under a shifting environment. We assume that the habitats of the involved species remain favorable over time, which ensures their eventual coexistence. First, under specific parameter conditions, the Hamilton–Jacobi method based on viscosity solutions is employed to determine the explicit formulas for the asymptotic spreading speed of the predator population. Subsequently, by utilizing the upper–lower solution method and the contracting rectangle method, we establish the existence of forced waves that satisfy the given boundary conditions. Finally, a contradiction argument is used to characterize the minimal wave speed of these forced waves.</p>

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Asymptotic spreading speeds and forced waves of a stage-structured predator–prey system in a shifting environment

  • 期刊论文

  • 发表日期：

    2026年4月25日

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  • Xiaoyi Chen,
  • Xiao Yu,
  • Liang Zhang

摘要

This work is devoted to the asymptotic spreading speed of predator populations and the existence/nonexistence of forced waves in a stage-structured predator–prey model under a shifting environment. We assume that the habitats of the involved species remain favorable over time, which ensures their eventual coexistence. First, under specific parameter conditions, the Hamilton–Jacobi method based on viscosity solutions is employed to determine the explicit formulas for the asymptotic spreading speed of the predator population. Subsequently, by utilizing the upper–lower solution method and the contracting rectangle method, we establish the existence of forced waves that satisfy the given boundary conditions. Finally, a contradiction argument is used to characterize the minimal wave speed of these forced waves.