Bifurcation control in small-world networks

In this paper, the problem of Hopf bifurcation control is considered for a small-world network model with time delays. We know that for the system without control, as the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller is proposed to delay the onset of an inherent bifurcation when such bifurcation is undesired. Numerical simulation results confirm that the new feedback controller using time delay is efficient in controlling Hopf bifurcation.