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

Cheng Hsiung Hsu, Suh Yuh Yang, Ting Hui Yang, Tzi Sheng Yang

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)


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.

頁(從 - 到)1472-1490
期刊Nonlinear Analysis: Real World Applications
出版狀態已出版 - 6月 2010


深入研究「Stability and bifurcation of a two-neuron network with distributed time delays」主題。共同形成了獨特的指紋。