Analysis of Bifurcation and Stability on Solutions of a Lotka-Volterra Ecological System with Cubic Functional Responses and Diffusion

Abstract

This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semi-trivial solutions by using spectrum analysis. Taking the growth rate as a bifurcation parameter and using the bifurcation theory, we discuss the existence and stability of the bifurcating solutions which emanate from the semi-trivial solutions.