一维Hopfield神经网络模型的多稳态分析

Multistable analysis for one dimensional Hopfield neural networks

摘要:

该文讨论一维Hopfield神经网络模型的多稳态问题.当模型所含S型激活函数没有有界性限制时,该文首先讨论了模型平衡点的存在性,并进一步给出了模型取得一个, 二个, 或三个平衡点的参数条件以及每个平衡点的稳定性.然后该文获得了模型在参数所有取值情况下的平衡点个数及其稳定性的结论.最后, 通过两个实例及其数值模拟说明了结论的有效性.

Abstract:

This paper focuses on multistable analysis of one dimensional Hopfield neural networks, whose sigmoid activation function may not be bounded. Firstly, the condition for the existence of equilibria is established. Moreover, the conditions for exactly 1, 2, or 3 equilibria and their stability respectively are proposed with some constraints for network parameters. Then, the corresponding results about the equilibria features are supplemented in the remaining cases for the parameters. Thus, we obtain the relationships between all the different values of the parameters and the number of equilibria as well as their stability. Finally, by employing bounded and unbounded activation functions, two examples and numerical simulations are used to illustrate the theory developed in this paper.