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Neural Processing Letters

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06-01-2018

Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays

Authors: Zhen Wang, Li Li, Yuxia Li, Zunshui Cheng

Published in: Neural Processing Letters | Issue 3/2018

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Abstract

In this paper, a class of three-neuron network with discrete and distributed delays is introduced. We first give a detailed Hopf bifurcation analysis for the proposed network. Choosing the discrete time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Moreover, by using the normal form theory and center manifold theorem, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived. Finally, numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

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Title: Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays
Authors: Zhen Wang
Li Li
Yuxia Li
Zunshui Cheng
Publication date: 06-01-2018
Publisher: Springer US
Published in: Neural Processing Letters / Issue 3/2018
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-017-9754-8

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