Asymptotic Stability of Multi-patch Predation Systems with Predator’s Diffusion and Evolution

• Chuhan Lai ^[1] ; Shikun Wang ^[2] ; Yuanshi Wang ^[1]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
  2. [2] Columbia University

     Columbia University

     Estados Unidos

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Predator-prey systems are considered in this work, where the predator moves between multiple patches with diffusion and evolution. By using dynamical systems theory and graph-theoretic method, we show that the system either admits a globally stable positive equilibrium, or has a globally stable boundary equilibrium. Further analysis on the model demonstrates that varying the asymmetric diffusion could lead to dynamics transitions between persistence of two species, survival of prey only in some of the patches, and extinction of prey in the system. A novel prediction of this work is that appropriate diffusion of predator could make both species reach total population sizes larger than those without diffusion, inappropriate diffusion would make both species approach total sizes less than those without diffusion, while other diffusions would make one species reach a larger size but make the other reach a less one. Evolution on the diffusive asymmetry by monotonic selection would make the predator reach a locally/globally maximal size, and make the patch network approach an evolutionary stable structure where any small deviation to it will not lead to the increase of species’ total size. Numerical simulations illustrate and extend our results. These results has potential applications in preserving biodiversity and ecological management.

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