Stability Of Steady State And Hopf Bifurcation In A Higher Order Autocatalator Reaction-Diffution System

A reaction-diffusion system based on the higher order autocatalator was studied in this paper. We discussed the stability of the steady state,then we using the Hopf bifurcation theorem studied the existence, direction, stability, cycle and other issues of the Hopf bifucation when the branch parameter changed. Reaction-diffusion system ,when parameters changes, the occurrence, direction, and cycle of the Hopf bifurcation.