Bifurcation analysis on a two-neuron system with distributed delays

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

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Author(s)

  • Xiaofeng Liao
  • Kwok-Wo Wong
  • Zhongfu Wu

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)123-141
Journal / PublicationPhysica D: Nonlinear Phenomena
Volume149
Issue number1-2
Publication statusPublished - 1 Feb 2001

Abstract

A general two-neuron model with distributed delays is studied in this paper. Its local linear stability is analyzed by using the Routh-Hurwitz criterion. If the mean delay is used as a bifurcation parameter, we prove that Hopf bifurcation occurs for a 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 determined by the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical analysis are also given.

Citation Format(s)

Bifurcation analysis on a two-neuron system with distributed delays. / Liao, Xiaofeng; Wong, Kwok-Wo; Wu, Zhongfu.

In: Physica D: Nonlinear Phenomena, Vol. 149, No. 1-2, 01.02.2001, p. 123-141.

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