Dynamical Behavior for an Extended Boissonade-De Kepper Model

Abstract

In this paper, an extended Boissonade-De Kepper model with discrete delays is considered. By linearizing the system at the equilibrium point and analyzing the instability of the linearized system, two sufficient conditions to guarantee the existence of periodic solutions of the system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation. Some numerical simulations are provided to illustrate our theoretical prediction. An interesting problem is solved.