Bogdanov–Takens Singularity in Tri-Neuron Network With Time Delay
Bogdanov–Takens Singularity in Tri-Neuron Network With Time Delay
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DOI：
10.1109/tnnls.2013.2238681
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发表时间：
2013-03
影响因子：
10.4
通讯作者：
Xing He;Chuandong Li;Tingwen Huang;C. Li
中科院分区：
文献类型：
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作者：
Xing He;Chuandong Li;Tingwen Huang;C. Li
本文利用时滞泛函微分方程对具有时滞的三神经元网络进行建模。利用中心流形约化和规范形方法研究了Bogdanov-Takens（B-T）分支。我们得到了该模型在B-T奇点处的范数形式的展开，并证明了该模型可以表现出干草叉、霍普夫、同宿和双极限环分支。给出了一些数值模拟来支持分析结果，并探讨混沌动力学。最后给出了一个算法，说明混沌三神经元网络可以用于彩色图像的加密。
This brief reports a retarded functional differential equation modeling tri-neuron network with time delay. The Bogdanov-Takens (B-T) bifurcation is investigated by using the center manifold reduction and the normal form method. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit pitchfork, Hopf, homoclinic, and double-limit cycles bifurcations. Some numerical simulations are given to support the analytic results and explore chaotic dynamics. Finally, an algorithm is given to show that chaotic tri-neuron networks can be used for encrypting a color image.