Monotone traveling waves for delayed Lotka-Volterra competition systems

Jian Fang; Jianhong Wu

doi:10.3934/dcds.2012.32.3043

Article Contents

2012, Volume 32, Issue 9: 3043-3058. Doi: 10.3934/dcds.2012.32.3043

This issue Previous Article The efficient approximation of coherent pairs in non-autonomous dynamical systems Next Article Relative entropies in thermodynamics of complete fluid systems

Monotone traveling waves for delayed Lotka-Volterra competition systems

Jian Fang^1, and
Jianhong Wu^2,

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001
2.
Centre for Disease Modelling and Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3

Received: January 2012

Revised: March 2012

Published: September 2012

Abstract / Introduction Related Papers Cited by

Abstract

We consider a delayed reaction-diffusion Lotka-Volterra competition system which does not generate a monotone semiflow with respect to the standard ordering relation for competitive systems. We obtain a necessary and sufficient condition for the existence of traveling wave solutions connecting the extinction state to the coexistence state, and prove that such solutions are monotone and unique (up to translation).

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Mathematics Subject Classification: Primary: 35R10, 35K57; Secondary: 92D25.

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