Stability and Hopf bifurcation of three-triangle neural networks with delays

In this paper, a neural networks model with seven neurons and time delay is considered. The model can be described as three triangles sharing one node. The local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. By using the de...

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Bibliographic Details
Published inNeurocomputing (Amsterdam) Vol. 322; pp. 206 - 215
Main Authors Cheng, Zunshui, Xie, Konghe, Wang, Tianshun, Cao, Jinde
Format Journal Article
LanguageEnglish
Published Elsevier B.V 17.12.2018
Subjects
Delays
Hopf Bifurcation
Neural networks
Neural networks
Hopf Bifurcation
Delays
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Summary:In this paper, a neural networks model with seven neurons and time delay is considered. The model can be described as three triangles sharing one node. The local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. By using the delay as bifurcation parameter, the critical value of bifurcation is given, and then the stability and Hopf bifurcation of the model are discussed. In addition, the stability and bifurcation direction of the bifurcation periodic solution are discussed by using the central manifold theorem and the norm form. The validity of the above theoretical results is verified by numerical simulation.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2018.09.063