Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

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

Pages: 1107 - 1131, Volume 10, Issue 5, October 2017      doi:10.3934/dcdss.2017060

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Hui Xue - College of Science, National University of Defense Technology, Changsha 410073, China (email)
Jianhua Huang - College of Science, National University of Defense Technology, Changsha, 410073, China (email)
Zhixian Yu - College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China (email)

Abstract: 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. Ikehara┼Ť 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.

Keywords:  Invasion traveling wave solutions, diffusive competition systems, existence, asymptotic behavior, uniqueness.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 35R10.

Received: December 2016;      Revised: January 2017;      Available Online: June 2017.