Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays
Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays
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DOI：
10.1016/j.amc.2018.02.029
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Li Li-Li;Zhen Wang;Yuxia Li;Hao Shen;Junwei Lu
中科院分区：
文献类型：
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作者：
Li Li-Li;Zhen Wang;Yuxia Li;Hao Shen;Junwei Lu
本文提出了一类具有离散和分布时滞的复值神经网络模型。以离散时滞为分支参数，在激活函数可分为真实的和虚部的假设下，研究了新提出的复值神经网络模型的Hopf分支问题.基于规范形理论和中心流形定理，建立了确定系统Hopf分支方向和分支周期解稳定性的充分条件.最后，通过数值算例验证了理论结果的有效性.
In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results.