Stability of the Brusselator model with delayed feedback control

Abstract. The classical diffusive Brusselator model has been extensively discussed even under the presence of certain types of discrete time-delays. However, models assuming delayed feedback have only been studied under certain highly restrictive conditions due to the computational complexity. In this paper, the stability of the unique equilibrium solution of the model is examined in a more general case, leaving the mentioned conditions out of consideration. When this type of delay is introduced, the original system of differential equations (system without delay) also substantially changes. Therefore, the ordinary system is considered in the absence of delay, and then it is examined whether the stability of the equilibrium solution changes when delay is assumed. In the investigations the focus is mainly on the existence of Hopf bifurcation.