Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 38, pp. 1-19.

Title: Traveling waves of a diffusive modified Leslie-Gower model with chemotaxis

Authors: Shuna Wang (Jiangsu Normal Univ., Xuzhou, Jiangsu, China)
         Jiang Liu (Jiangsu Normal Univ., Xuzhou, Jiangsu, China)
         Jun Fang (Jiangsu Normal Univ., Xuzhou, Jiangsu, China)
         Xiaojie Lin (Jiangsu Normal Univ., Xuzhou, Jiangsu, China)

Abstract:
In this article, we study a diffusive modified Leslie-Gower model with 
chemotaxis and large wave speed. By applying traveling wave transformation 
and changing the time scale, this  modified Leslie-Gower model can be 
transformed into a singularly perturbed system. We establish the existence 
of heteroclinic orbits connecting different equilibria for the system without 
perturbation by constructing invariant regions and using the 
Poincare-Bendixson theorem. Then the existence of traveling wave 
solutions  for the diffusive modified Leslie-Gower system is demonstrated 
via the geometric singular perturbation theory and  Fredholm theory.

Submitted February 21, 2025. Published April 10, 2025.
Math Subject Classifications: 35K57, 92D25, 35C07, 34D15.
Key Words: Modified Leslie-Gower model; chemotaxis; traveling waves; geometric singular perturbation.