Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays

被引：8
|
作者：
Han, Yanyan [1 ]
Song, Yongli [1 ]
机构：
[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China
来源：
NONLINEAR DYNAMICS | 2012年 / 69卷 / 1-2期
关键词：
Neural network; Distributed delay; Stability; Hopf bifurcation; BAM NEURAL-NETWORK; PERIODIC-SOLUTIONS; SPATIOTEMPORAL PATTERNS; NONLINEAR OSCILLATIONS; 2-NEURON SYSTEM; NEURONS; EXISTENCE; DYNAMICS; FEEDBACK; ORBITS;
D O I：
10.1007/s11071-011-0269-y
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
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.
引用
收藏
页码：357 / 370
页数：14
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