Stability switching and Hopf bifurcation in a multiple-delayed neural network with distributed delay
Stability switching and Hopf bifurcation in a multiple-delayed neural network with distributed delay
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DOI：
10.1016/j.jmaa.2013.05.021
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发表时间：
2013-11
影响因子：
1.3
通讯作者：
I. Ncube
中科院分区：
文献类型：
--
作者：
I. Ncube
我们考虑一个包含分布式和离散信号传输延迟的三个相同神经元的网络。这种网络的模型是一个耦合的非线性时滞微分方程组。由于网络的D3对称性，在系统的平凡平衡点可能出现两种单Hopf分叉。这些单Hopf分支是单根和重根。本文从简单根的情况出发，讨论了平凡平衡点的绝对稳定性和稳定性切换问题，给出了临界时滞的计算和Hopf分支定理的表述。
We consider a network of three identical neurons incorporating distributed and discrete signal transmission delays. The model for such a network is a system of coupled nonlinear delay differential equations. It is established that two cases of a single Hopf bifurcation may occur at the trivial equilibrium of the system, as a consequence of the D3symmetry of the network. These single Hopf bifurcations are the simple and the double root. The present paper looks at the simple root case, and addresses the issue of absolute stability of the trivial equilibrium and stability switching, leading up to calculation of the critical delay and formulation of a Hopf bifurcation theorem.