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

Min Xiao1, Binbin Tao1, Wei Xing Zheng2

  • 1Nanjing University of Posts and Telecommunications
  • 2Western Sydney University


10:30 - 10:50 | Tue 20 August | Lau, 5-206 | TuA5.1

Session: Network Systems

Category: Regular Session

Full Text


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.