Frequency domain approach to computational analysis of bifurcation and periodic solution in a two-neuron network model with distributed delays and self-feedbacks

Min Xiao, Wei Xing Zheng, Jinde Cao

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    In this paper, a general two-neuron model with distributed delays, self-feedbacks and a weak kernel is studied. It is shown that the Hopf bifurcation occurs as the bifurcation parameter, the mean delay, passes a critical value where a family of periodic solutions emanate from the equilibrium. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of the bifurcation critical point of the mean delay is determined. The direction and the stability of bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Numerical simulation results supporting the theoretical analysis are also given.
    Original languageEnglish
    Pages (from-to)206-213
    Number of pages8
    JournalNeurocomputing
    Volume99
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Hopf bifurcation
    • Nyquist criterion
    • distributed delays
    • frequency domain
    • neural network
    • neuron
    • peiodic solutions
    • stability

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