Stability and Bifurcation of a Two-Neuron Network with Distributed Time Delays
學年 98
學期 2
出版（發表）日期 2010-06-01
作品名稱 Stability and Bifurcation of a Two-Neuron Network with Distributed Time Delays
作品名稱（其他語言）
著者 Hsu, Cheng-Hsiung; Yang, Suh-Yuh; Yang, Ting-Hui; Yang, Tzi-Sheng
單位 淡江大學數學學系
出版者 London: Elsevier Ltd
著錄名稱、卷期、頁數 Nonlinear Analysis: Real World Applications 11(3), pp.1472-1490
摘要 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.
關鍵字 Neural network; Distributed time delay; Characteristic equation; Hopf bifurcation; Pitchfork bifurcation; Normal form
語言 en
ISSN 1468-1218
期刊性質 國外
收錄於 EI SCI
產學合作
通訊作者 Yang, Suh-Yuh
審稿制度 是
國別 GBR
公開徵稿
出版型式 紙本
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