Hopf Bifurcation in Small-World Network Model via Time-Delayed Feedback Control

Abstract

In this paper, we study the bifurcation control in a small-world network with time delay. The time delay is chosen as its bifurcation parameter, and the characteristic equation is analyzed to construct the conditions of the stability and Hopf bifurcation. We find that the onset of Hopf bifurcation can be advanced or delayed by adjusting the parameter of the delayed feedback control. Finally, numerical simulations are carried out to verify the theoretical analysis. Moreover, the relationship between the control parameter and the onset of bifurcation is given.