Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 33, pp. 1-19.

Title: Dynamics of traveling waves for predator-prey systems with Allee effect and time delay

Authors: Yang Hua (Jiangsu Normal Univ., Xuzhou, China)
         Xiaojie Lin (Jiangsu Normal Univ., Xuzhou, China)
         Jiang Liu (Jiangsu Normal Univ., Xuzhou, China)
         Haixia Lu (Jiangsu Normal Univ., Xuzhou, China)

Abstract: 
This article aims to establish the existence of traveling waves for a 
predator-prey system with Beddington-DeAngelis functional response, reproductive
Allee effect, and time delay. We investigate the existence of solutions for a system 
with two special delay kernels by geometric singular perturbation theory, 
invariant manifold theory, and Fredholm orthogonality theory. In addition,
we discuss the asymptotic behaviors of traveling waves with the aid of the asymptotic 
theory.


Submitted November 29, 2023. Published April 26, 2024.
Math Subject Classifications: 92D25, 35C07, 35K57, 34D15.
Key Words: Predator-prey system; Allee effect; traveling waves; asymptotic behavior; geometric singular perturbation.