On Hopf bifurcation and control for a delay systems

摘要

Hopf bifurcation of a delay differential equation modeling two-enterprise interaction mechanism is investigated. For the demands of computer simulation applications, the discrete-time two-enterprise interaction model is proposed by using the forward Euler scheme. By discussing the characteristic equation of linearized part, the local stability criterion of the positive fixed point is presented. Time lag is selected as the bifurcation parameter. Then it is demonstrated that variation of time lag may result in Hopf bifurcation. Furthermore, derivations for the directions and stability of Hopf bifurcation are also given. For the purpose of controlling Hopf bifurcation, a time-delayed feedback control scheme is proposed. Finally, we simulate the main results.