# American Institute of Mathematical Sciences

October  2017, 10(5): 1107-1131. doi: 10.3934/dcdss.2017060

## Invasion traveling wave solutions in temporally discrete random-diffusion systems with delays

 1 College of Science, National University of Defense Technology, Changsha 410073, China 2 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

* Corresponding author: Jianhua Huang

Received  December 2016 Revised  January 2017 Published  June 2017

Fund Project: * The first two authors are supported by the NSF of China(No.11371367,11571126), and the third author is supported by Innovation Program of Shanghai Municipal Education Commission (No.14YZ096) and by the Hujiang Foundation of China (B14005)

This paper is devoted to the invasion traveling wave solutions for a temporally discrete delayed reaction-diffusion competitive system. The existence of invasion traveling wave solutions is established by using Schauder's fixed point Theorem. Ikeharaś theorem is applied to show the asymptotic behaviors. We further investigate the monotonicity and uniqueness invasion traveling waves with the help of sliding method and strong maximum principle.

Citation: Hui Xue, Jianhua Huang, Zhixian Yu. Invasion traveling wave solutions in temporally discrete random-diffusion systems with delays. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1107-1131. doi: 10.3934/dcdss.2017060
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