Dynamic optimal control at Hopf bifurcation of a Newman-Watts model of small-world networks via a new PD1/n scheme

摘要

In this paper, a neoteric fractional-order Proportional-Derivative (PD) feedback controller is proposed to address the problem of bifurcation control for an integer-order small-world network model with discrete delay. The time delay is selected as the bifurcation parameter, and sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed by analyzing the stability of the controlled system. By regulating the controller parameters, the dynamic behavior for the controlled system can be effectively optimized. Finally, by simulating numerical examples, theoretical derivations are verified and the relationships between the onset of the Hopf bifurcation and the controller parameters are obtained. (C) 2019 Elsevier B.V. All rights reserved.