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January  2012, 17(1): 173-189. doi: 10.3934/dcdsb.2012.17.173

## Traveling wave solutions of a competitive recursion

 1 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000 2 School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received  April 2010 Revised  March 2011 Published  October 2011

This paper is concerned with the traveling wave solutions of a competitive recursion. By using a cross iteration scheme, we first establish the existence of traveling wave solutions, which are the invasion waves of two competitive invaders. These wave solutions are useful in understanding the long time behavior of solution of the corresponding Cauchy type problem where the initial distribution is a perturbation of the wave profile of a traveling wave solution that may be nonmonotone.
Citation: Guo Lin, Wan-Tong Li. Traveling wave solutions of a competitive recursion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 173-189. doi: 10.3934/dcdsb.2012.17.173
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