A REVIEW ON THE DYNAMICS OF TWO SPECIES COMPETITIVE ODE AND PARABOLIC SYSTEMS

Abstract

This paper is devoted to a review on the dynamics of two species competition systems including the classical ODE, reaction-diffusion as well as reaction-diffusion-advection models. The primary purpose is to illustrate the effect of competition intensity, movement (diffusion and/or advection) and spatial variation on the population dynamics. Specific topics include LotkaVolterra competition models in heterogeneous environments and in advective environments, linear second order eigenvalue problems, and the evolution of movement strategy. Several fundamental tools such as the monotone theory, the principal eigenvalue theory (for single equations or systems) and some technical approaches are introduced. Some recent developments are discussed and also several problems that deserve future investigation are proposed.