A geometric approach in the study of traveling waves for some classes of non-monotone reaction-diffusion systems

摘要

In this paper we further extend a recently developed method to investigate the existence of traveling waves solutions and their minimum wave speed for non-monotone reaction diffusion systems. Our approach consists of two steps. First we develop a geometrical shooting argument, with the aid of the theorem of homotopy invariance on the fundamental group, to obtain the positive semi-traveling wave solutions for a large class of reaction diffusion systems, including the models of predator prey interaction (for both predator-independent/dependent functional responses), the models of combustion, Belousov-Zhabotinskii reaction, SI-type of disease transmission, and the model of biological flow reactor in chemostat. Next, we apply the results obtained from the first step to some models, such as the Beddinton-DeAngelis model and the model of biolocal flow reactor, to show the convergence of these semi-traveling wave solutions to an interior equilibrium point by the construction of a Lyapunov-type function, or the convergence of semi traveling waves to another boundary equilibrium point by the further analysis of the asymptotical behavior of semi-traveling wave solutions. (C) 2015 Elsevier Inc. All rights reserved.