School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China.
Neural Netw. 2018 Jan;97:116-126. doi: 10.1016/j.neunet.2017.09.013. Epub 2017 Oct 14.
This paper provides new theoretical results on the multistability and instability analysis of recurrent neural networks with time-varying delays. It is shown that such n-neuronal recurrent neural networks have exactly [Formula: see text] equilibria, [Formula: see text] of which are locally exponentially stable and the others are unstable, where k is a nonnegative integer such that k≤n. By using the combination method of two different divisions, recurrent neural networks can possess more dynamic properties. This method improves and extends the existing results in the literature. Finally, one numerical example is provided to show the superiority and effectiveness of the presented results.
本文针对时变时滞递归神经网络的多稳定性和不稳定性分析提供了新的理论结果。研究表明，这种 n 神经元递归神经网络恰好有 [Formula: see text] 个平衡点，其中 [Formula: see text] 个是局部指数稳定的，其余的是不稳定的，其中 k 是一个非负整数，使得 k≤n。通过使用两种不同划分的组合方法，递归神经网络可以具有更多的动态特性。该方法改进和扩展了现有文献中的结果。最后，通过一个数值例子来说明所提出结果的优越性和有效性。
