IEEE Trans Neural Netw Learn Syst. 2013 Jun;24(6):1001-7. doi: 10.1109/TNNLS.2013.2238681.
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.
这篇简报报告了一个具有时滞的三神经元网络的迟滞泛函微分方程模型。利用中心流形约化和规范形方法研究了 Bogdanov-Takens（B-T）分岔。我们得到了 B-T 奇点处规范形的普遍展开，并表明该模型可以表现出叉分、Hopf、同宿和双极限环分岔。给出了一些数值模拟结果以支持解析结果并探索混沌动力学。最后，给出了一个算法来表明混沌三神经元网络可用于加密彩色图像。
