Travelling Waves for a Diffusive Lotka-Volterra Competition Model II: A Geometric Approach

Yuzo Hosono

Department of Information and Communication Sciences, Kyoto Sangyo University, Kyoto 603, Japan

(Received November 15, 1995; Accepted December 20, 1995)

Keywords: Travelling Wave, Lotka-Volterra Model, Competition, Minimal Wave Speed

Abstract. This paper concerns travelling wave solutions for a two competing species model. The model system has the Lotka-Volterra type interaction term and is assumed to have linear diffusion only in the species which is the stronger one. By the shooting method based on the Wazewski theorem, we give the minimal speed c_min such that travelling wave solutions exist only for each c c_min under an appropriate condition on parameters appearing in the equations.