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

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

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5 Scopus citations


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.

Original languageEnglish
Pages (from-to)1472-1490
Number of pages19
JournalNonlinear Analysis: Real World Applications
Issue number3
StatePublished - Jun 2010


  • Characteristic equation
  • Distributed time delay
  • Hopf bifurcation
  • Neural network
  • Normal form
  • Pitchfork bifurcation


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