Coexistence and local -stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays

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• 作者：Xiaobing Nie^a ; ^b ; ^{xbnie@seu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Wei Xing Zheng^b ; ^{w.zheng@westernsydney.edu.au" class="auth_mail" title="E-mail the corresponding author} ; Jinde Cao^a ; ^{jdcao@seu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Memristive neural networks ; Multistability ; μμ-stability ; Nonmonotonic piecewise linear activation functions ; Unbounded time delays
• 刊名：Neural Networks
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：84
• 期：Complete
• 页码：172-180
• 全文大小：1068 K

文摘

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n$n$-neuron MNNs can have 5ⁿ$5^n$ equilibrium points located in ℜⁿ${\Re }^n$, and 3ⁿ$3^n$ of them are locally μ$\mu$-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log–log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results.