July  2007, 8(1): 115-125. doi: 10.3934/dcdsb.2007.8.115

Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems

1. 

Department of Information and Communication Sciences, Kyoto Sangyo University, Kyoto 603-8555

Received  November 2005 Revised  February 2006 Published  April 2007

This paper investigates the existence of travelling waves for the two component higher order autocatalytic reaction-diffusion systems by the phase plane analysis. We prove the existence of travelling waves for the system without decay for two extreme cases: the non-diffusive reactant case and the equal diffusive case. We further discuss the existence problem for the system with higher order decay when the reactant does not diffuse. Our analysis also gives the estimate of the minimal propagation speeds in terms of the order of autocatalysis.
Citation: Yuzo Hosono. Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 115-125. doi: 10.3934/dcdsb.2007.8.115
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