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July  2010, 14(1): 111-128. doi: 10.3934/dcdsb.2010.14.111

Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type

1. 

Department of Mathematics, National Central University, Chung-Li 32001, Taiwan

2. 

Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137, Taiwan

Received  March 2009 Revised  January 2010 Published  April 2010

In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c *, and show the existence of traveling plane wave solutions connecting two different equilibria when the wave speeds are large than c *.
Citation: Cheng-Hsiung Hsu, Ting-Hui Yang. Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 111-128. doi: 10.3934/dcdsb.2010.14.111
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