Existence And Stability Of Trveling Wave Solutions For Several Types Of Population Models

In this paper, we discuss existence and stability of traveling wave solutions for several types of reaction diffusion systems by using the perturbation method. This paper is divided into four parts.In chapter 1, we briefly introduce the background and meaningful of the problems investigated in this thesis and give preliminaries. In chapter 2, we study the existence of traveling fronts solutions of the Nicholson's butterflies equation with diffusion and a single delay. Sufficient conditions for the existence of traveling wave solutions are obtained.Chapter 3 is devoted to analyze the stability of the positive equilibrium for Phytoplankton-Zooplankton model. The results show that diffusion can't drive instabi-lity of the system.In chapter 4, we consider the stability of wavefront solutions for the Nagumo's equation under small perturbations of the waveform by the perturbation method. Sufficient conditions for the stability of wave front solutions are obtained.