Bifurcation Analysis Of A Belousov-Zhabotinskii Diffusion Model In R~3

Belousov-Zhabotinskii reaction is a very typical chemical oscillating reaction,and named after two Russian scientists,it was first discovered by chemist Belousov.Meanwhile,during the reaction process,it was found that the concentration of reactants would exhibit the property of periodic oscillation.By means of partial differential equation and dynamic system,this paper studies the global dynamic behavior of BZ reaction diffusion equations with spatial form,explains the formation mechanism of periodic oscillation by proving the existence of periodic solutions,and simulates abundant pattern forms.In this paper,we consider the Belousov-Zhabotinskii(BZ for short)system in R3 and study positive constant solution for this model.We can obtain the global stability of this solution by establishing the Lyapunov function through the lin-earization theory and prove the existence of Hopf bifurcation and the stability of Hopf bifurcation by using bifurcation theory,central manifold and other theories.