Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

39 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)319-344
Journal / PublicationNonlinear Dynamics
Volume58
Issue number1-2
Publication statusPublished - Oct 2009

Link(s)

Abstract

We show that time-delayed feedback methods, which have successfully been used to control unstable steady states or periodic orbits, provide a tool to control Hopf bifurcation for a small-world network model with nonlinear interactions and time delays. We choose the interaction strength parameter as a bifurcation parameter. Without control, bifurcation will occur early; meanwhile, the model can maintain a stationary total influenced volume only in a certain domain of the interaction strength parameter. However, outside of this domain the model still possesses a stable total influenced volume that can be guaranteed by delayed feedback perturbation, and the onset of the Hopf bifurcation is postponed. The feedback perturbation vanishes if the stabilization is successful and thus the domain of stability can be extended under only small control force. We present an analytical investigation of the feedback scheme using characteristic equation and discuss effects of both a low-pass filter included in the control loop and nonzero latency times associated with generation and injection of the feedback signal.

Research Area(s)

  • Bifurcation control, Hopf bifurcation, Latency time, Low-pass filter, Small-world network, Time-delayed feedback

Citation Format(s)

Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation. / Xiao, Min; Ho, Daniel W. C.; Cao, Jinde.
In: Nonlinear Dynamics, Vol. 58, No. 1-2, 10.2009, p. 319-344.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

Download Statistics

No data available