Hopf bifurcation on a two-neuron system with distributed delays : A frequency domain approach

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

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Author(s)

  • Xiaofeng Liao
  • Shaowen Li
  • Kwok-Wo Wong

Detail(s)

Original languageEnglish
Pages (from-to)299-326
Journal / PublicationNonlinear Dynamics
Volume31
Issue number3
Publication statusPublished - Feb 2003

Abstract

In this paper, a more general two-neuron model with distributed delays and weak kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, we found that if the mean delay is used as a bifurcation parameter, Hopf bifurcation occurs for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given.

Research Area(s)

  • Distributed delays, Graphical Hopf bifurcation theorem, Hopf bifurcation, Neuron, Nyquist criterion, Periodic solutions

Citation Format(s)

Hopf bifurcation on a two-neuron system with distributed delays: A frequency domain approach. / Liao, Xiaofeng; Li, Shaowen; Wong, Kwok-Wo.
In: Nonlinear Dynamics, Vol. 31, No. 3, 02.2003, p. 299-326.

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