# American Institute of Mathematical Sciences

September  2012, 32(9): 3043-3058. doi: 10.3934/dcds.2012.32.3043

## Monotone traveling waves for delayed Lotka-Volterra competition systems

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

Received  January 2012 Revised  March 2012 Published  April 2012

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).
Citation: Jian Fang, Jianhong Wu. Monotone traveling waves for delayed Lotka-Volterra competition systems. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3043-3058. doi: 10.3934/dcds.2012.32.3043
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##### References:
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