链式神经网络动力学及其与环状结构、星型结构对比分析

Dynamics of chain-structure neural networks and its comparative analysis with different structures of ring and star

中文关键词  分岔动力学  链式结构  神经网络  多时滞  流图分解

英文关键词  bifurcation dynamics  chain structures  neural networks  multiple delays  flow graph decomposition

中文摘要

      链式结构作为一种基本结构广泛地存在于各种复杂系统当中, 然而, 对于链式结构的复杂网络动力学分析鲜有报道. 本文以神经网络为例, 研究具有链式结构的多时滞高维神经网络模型的分岔动力学, 并运用流图分解法以及整体元替代法推导出特征多项式随神经元节点个数变化的递推规律式, 从而分析出特征多项式方程根的分布情况. 考虑神经递质传输时延对系统稳定性的影响, 并得出导致系统拓扑突变的临界值. 最后, 通过数值仿真验证给出理论的正确性, 并通过对比仿真对链式结构、星型结构与环形结构这3种结构的神经网络动力学进行分析, 从而得出神经网络的结构性差异对网络分岔动力学的影响.

英文摘要

      The chain structure widely exists in various complex systems, however, there are few studies on the bifurcation dynamics of complex networks with chain structure. Taking neural network as an example, this paper studies the bifurcation dynamics of high-dimensional neural network models with chain structure and multiple delays. The recursion formulas of the characteristic polynomial varying with the number of neuron nodes is listed by the methods of the flow graph decomposition and global element substitution. Thereby, the distribution of the roots on the characteristic polynomial equation is analyzed. Afterwards, considering the effect of neurotransmitter transmission delay on the stability of the system, the critical value leading to the topological mutation of the system is obtained. Finally, the correctness of the theories are verified by numerical simulations, and the dynamics on neural networks of different structures including chain structure, star structure and ring structure are analyzed in comparison with simulated experiments for acquiring the influence of structural differences on bifurcation dynamics of neural networks.