# American Institute of Mathematical Sciences

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## Traveling wave fronts in a diffusive and competitive Lotka-Volterra system

 School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

* The corresponding author

Received  March 2019 Revised  December 2020 Published  January 2021

Fund Project: This work is partially supported by the Natural Science Foundation of China (Grant Nos. 11871251, 12090011 and 11801231)

In this paper, we consider a two-species competitive and diffusive system with nonlocal delays. We investigate the existence of traveling wave fronts of the system by employing linear chain techniques and geometric singular perturbation theory. The existence of the traveling wave fronts analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a six-dimensional system without delay.

Citation: Zengji Du, Shuling Yan, Kaige Zhuang. Traveling wave fronts in a diffusive and competitive Lotka-Volterra system. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021010
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