Dynamic Bufurcation of a Tri-molecular Autocatalytic Reaction-diffusion System

Abstract

The tri-molecular autocatalytic reaction-diffusion system is a class of model, which can reveal a variety of phenomena observed in areas of encompassing physics, biology, ecology, chemistry and many other fields. In this paper, the tri-molecular autocatalytic reaction-diffusion system with Neumann boundary condition is studied. First, We have reached the following conclusion: the equilibrium of the system loses stability if the parameter is greater than a fixed value, and the corresponding principle of exchange stability condition is then verified. Second, we obtained the local asymptotic stability of trivial, transition types, expressions of bifurcated solutions, the main tools are center manifold theory. The theory is used to reduce the infinite dynamical system to a finite dimensional. Finally, the necessary explanations for the theory is provided.