Stability and bifurcation of a two-neuron network with distributed time delays

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51151

Title:	Stability and bifurcation of a two-neuron network with distributed time delays
Authors:	Hsu,CH;Yang,SY;Yang,TH;Yang,TS
Contributors:	數學系
Keywords:	FUNCTIONAL-DIFFERENTIAL EQUATIONS;ALMOST-PERIODIC SOLUTIONS;CELLULAR NEURAL NETWORKS;EXPONENTIAL STABILITY;NORMAL FORMS;EXISTENCE;DYNAMICS;NEURONS;SYSTEM;MODEL
Date:	2010
Issue Date:	2012-03-27 18:23:23 (UTC+8)
Publisher:	國立中央大學
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. (C) 2009 Elsevier Ltd. All rights reserved.
Relation:	NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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