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

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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

Cheng-Hsiung Hsu ^1, and Ting-Hui Yang ^2,

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

Abstract
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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 ^*.

Keywords: Traveling Wave Solution, Heteroclinic Solutions., Delayed Lattice Differential Equations, Upper And Lower Solutions.

Mathematics Subject Classification: Primary: 34A33, 34C37, 34K10, 35C07; Secondary: 92B2.

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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