Traveling Wave Solution of a Reaction–Diffusion Predator–Prey System

Liu, Jiang ^[1] ; Xu, Dongcheng ^[1] ; Du, Zengji ^[1]
1. [1] Jiangsu Normal University
  
  Jiangsu Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 57-67
Idioma: inglés
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Resumen
- In this paper, we discuss a reaction–diffusion predator–prey model with nonlocal delays. By using the theory of dynamical systems, specifically based on geometric singular perturbation theory, center manifold theorem and Fredholm theory, we construct an invariant manifold for the associated predator–prey equation and use this invariant manifold to obtain a heteroclinic orbit between two non-negative equilibrium points. Furthermore, we establish the existence result of traveling wave solution for the predator–prey model.