PID Control of Hopf Bifurcation of Delayed Small-World Networks with Fractional-Order Dynamics

Abstract

This paper investigates the problem of controlling Hopf bifurcation of delayed small-world networks with fractional-order dynamics. Specifically, a fractional-order PID feedback controller is designed to realize control of the Hopf bifurcation that is embedded in delayed small-world networks with fractional-order dynamics. The characteristic equation of the controlled fractional-order network is analyzed, which yields the useful conditions for stability as well as Hopf bifurcation. Moreover, the analysis reveals that the control parameters of the fractional-order PID feedback control scheme may be varied to have a significant effect on the bifurcation dynamics of the controlled small-world network with fractional-order dynamics. The theoretical findings are also confirmed through computer simulations.