Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays
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- 作者：Yanyan Han (1)
Yongli Song (1) syl.mail@163.com - 关键词：Neural network – ; Distributed delay – ; Stability – ; Hopf bifurcation
- 刊名：Nonlinear Dynamics
- 出版年：2012
- 出版时间：July 2012
- 年：2012
- 卷：69
- 期：1-2
- 页码：357-370
- 全文大小：1.1 MB
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- 刊物类别：Engineering
- 刊物主题：Vibration, Dynamical Systems and Control
Mechanics
Mechanical Engineering
Automotive and Aerospace Engineering and Traffic - 出版者：Springer Netherlands
- ISSN：1573-269X
文摘
In this paper, we consider the effect of distributed delays in a three-neuron unidirectional ring. Sufficient conditions for existence of unique equilibrium, multiple equilibria and their local stability are derived. Taking the average delay as a bifurcation parameter, we find two critical values at which the system undergoes Hopf bifurcations. The orbital asymptotic stability of the Hopf bifurcating periodic solutions is investigated by using the method of multiple scales. The global Hopf bifurcation is also studied. Finally, the theoretical results are illustrated by some numerical simulations.