Communications on Pure and Applied Analysis (CPAA)

Traveling waves in a three species competition-cooperation system

Pages: 1103 - 1119, Volume 16, Issue 4, July 2017      doi:10.3934/cpaa.2017053

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Xiaojie Hou - Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403, United States (email)
Yi Li - Department of Mathematics, California State University Northridge, CA 91330, United States (email)

Abstract: This paper studies the traveling wave solutions to a three species competition cooperation system, which is derived from a spatially averaged and temporally delayed Lotka Volterra system. The existence of the traveling waves is investigated via a new type of monotone iteration method. The upper and lower solutions come from either the waves of KPP equation or those of certain two species Lotka Volterra system. We also derive the asymptotics and uniqueness of the wave solutions.

Keywords:  Traveling wave, spatio-temporal delay, Lotka Volterra, competition cooperation, existence.
Mathematics Subject Classification:  Primary: 35B40, 35B50, 35B51, 35K40, 35K57; Secondary: 35Q92.

Received: March 2014;      Revised: February 2017;      Available Online: April 2017.