Large-Scale Neural Networks With Asymmetrical Three-Ring Structure: Stability, Nonlinear Oscillations, and Hopf Bifurcation
研究了一类具有三个环和多个时滞的高维神经网络，每个环的神经元数量不同但共享一个公共节点，分析了时滞对稳定性和Hopf分岔的影响，发现环内神经元数和总神经元数均显著影响网络动态。
A large number of experiments have proved that the ring structure is a common phenomenon in neural networks. Nevertheless, a few works have been devoted to studying the neurodynamics of networks with only one ring. Little is known about the dynamics of neural networks with multiple rings. Consequently, the study of neural networks with multiring structure is of more practical significance. In this article, a class of high-dimensional neural networks with three rings and multiple delays is proposed. Such network has an asymmetric structure, which entails that each ring has a different number of neurons. Simultaneously, three rings share a common node. Selecting the time delay as the bifurcation parameter, the stability switches are ascertained and the sufficient condition of Hopf bifurcation is derived. It is further revealed that both the number of neurons in the ring and the total number of neurons have obvious influences on the stability and bifurcation of the neural network. Ultimately, some numerical simulations are given to illustrate our qualitative results and to underpin the discussion.