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Bistable Waves for a Gilpin-AyalaModel with Local Versus Nonlocal Diffusion

  • Hongyong Wang [1] ; Jiali Zhan [2] ; Yuting Wan [2]
    1. [1] Hunan First Normal College

      Hunan First Normal College

      China

    2. [2] University of South China

      University of South China

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 2, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • We investigate the existence, asymptotic exponential stability and propagation direction of the bistable traveling wave for a Gilpin-Ayala model with local versus nonlocal diffusion. The existence of the bistable travelingwaves of themodel is first established.

      Then, the asymptotic exponential stability of the bistable traveling wave is studied by using Chen’s method. However, we note that both the Jacobian matrices at the two stable equilibria of the corresponding kinetic system of the Gilpin-Ayala model are reducible. To overcome this difficulty, we employ a perturbation technique that can render the Jacobian matrices at the equilibrium points irreducible after perturbation. In addition, we provide a unified approach to prove that the bistable traveling waves are strictly monotonic. Based on the above two results, we show that the bistable traveling waves of the model are asymptotically-exponentially stable under certain restrictions on the initial conditions. Finally, we also find that the sign of the bistable wave speed is simply determined by the difference between the interspecific competition coefficients and is independent of the diffusion coefficient and intrinsic growth rate. The method employed in this paper can be applied to more general systems with mixed diffusions.

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