Stability and Hopf bifurcation in a state-dependent delayed Brusselator-type model

Abstract

In this paper, we study the local dynamical behavior of a Brusselatortype model with state-dependent delay. First, we investigate the local stability of the positive equilibrium and the existence of the Hopf bifurcation. Secondly, the asymptotic of the solutions near the equilibria are constructed by using the perturbation method which further determines the properties of Hopf bifurcation. Finally, the numerical simulations are carried out to support the theoretical findings.