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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/58792

    Title: Stability and Bifurcation of a Two-Neuron Network with Distributed Time Delays
    Authors: Hsu, Cheng-Hsiung;Yang, Suh-Yuh;Yang, Ting-Hui;Yang, Tzi-Sheng
    Contributors: 淡江大學數學學系
    Keywords: Neural network;Distributed time delay;Characteristic equation;Hopf bifurcation;Pitchfork bifurcation;Normal form
    Date: 2010-06
    Issue Date: 2011-10-01 21:11:32 (UTC+8)
    Publisher: London: Elsevier Ltd
    Abstract: In this paper we study the stability and bifurcation of the trivial solution of a two-neuron network model with distributed time delays. This model consists of two identical neurons, each possessing nonlinear instantaneous self-feedback and connected to the other neuron with continuously distributed time delays. We first examine the local asymptotic stability of the trivial solution by studying the roots of the corresponding characteristic equation, and then describe the stability and instability regions in the parameter space consisting of the self-feedback strength and the product of the connection strengths between the neurons. It is further shown that the trivial solution may lose its stability via a certain type of bifurcation such as a Hopf bifurcation or a pitchfork bifurcation. In addition, the criticality of Hopf bifurcation is investigated by means of the normal form theory. We also provide numerical evidence to support our theoretical analyses.
    Relation: Nonlinear Analysis: Real World Applications 11(3), pp.1472-1490
    DOI: 10.1016/j.nonrwa.2009.03.004
    Appears in Collections:[數學學系暨研究所] 期刊論文

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