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

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.