The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain
The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain
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DOI：
10.1016/j.neucom.2009.08.018
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发表时间：
2010
期刊：
影响因子：
6
通讯作者：
A. Hajihosseini;G. R. R. Lamooki-G.-R.-R.-Lamooki-3263715;Babak Beheshti;Farzaneh Maleki
中科院分区：
文献类型：
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作者：
A. Hajihosseini;G. R. R. Lamooki-G.-R.-R.-Lamooki-3263715;Babak Beheshti;Farzaneh Maleki
本文研究了一类具有分布式延迟和强核的循环神经网络。结果表明，Hopf 分岔发生在分岔参数（平均延迟）超过临界值时，其中一系列周期解源自平衡。此类解的存在性和稳定性由频域中的 Hopf 分岔定理和广义奈奎斯特稳定性准则确定。
In this paper, a class of recurrent neural networks with distributed delays and a strong kernel is studied. It is shown that the Hopf bifurcation occurs as the bifurcation parameter, the mean delay, passes a critical value where a family of periodic solutions emanates from the equilibrium. The existence and stability of such solutions are determined by the Hopf bifurcation theorem in the frequency domain and the generalized Nyquist stability criterion.