Dynamic Transition Analysis for Activator-Substrate System

Abstract

The main objective of this article is to study the dynamic transition associated with the activator-substrate system. Two criteria are derived to describe the transition from real eigenvalues or complex eigenvalues and the types of transition. Notably, we get two parameters b_{1} and b_{2}, which can determine the the types of transitions for the two criteria respectively. The analysis is carried out using dynamic transition theory developed recently by Ma and Wang (Phase transition dynamics, Springer, New York, 2013, Bifurcation Theory and Applications, World Scientific, Singapore, 2005, Stability and Bifurcation of Nonlinear Evolutions Equations, Science Press, Beijing, China, 2007).