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

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Regular Session

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10:30 - 12:30 | Tue 20 Aug | Lau, 5-206 | TuA5

Network Systems

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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.

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