Wang Dongshu, Huang Lihong, Tang Longkun
IEEE Trans Neural Netw Learn Syst. 2018 Aug;29(8):3815-3827. doi: 10.1109/TNNLS.2017.2741349. Epub 2017 Sep 14.
This paper is concerned with the dissipativity and synchronization problems of a class of delayed bidirectional associative memory (BAM) neural networks in which neuron activations are modeled by discontinuous bivariate functions. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides and mixed delays via functional differential inclusions. The global dissipativity of the Filippov solution to the considered BAM neural networks is proven using generalized Halanay inequalities and matrix measure approaches. Second, to realize global exponential complete synchronization of BAM neural networks with multivariate discontinuous activations, discontinuous state feedback controllers are designed using functional differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov functional method. Finally, several numerical examples are provided to demonstrate the applicability and effectiveness of our proposed results.
本文关注一类具有时滞的双向联想记忆（BAM）神经网络的耗散性和同步问题，其中神经元激活由不连续的二元函数建模。首先，通过泛函微分包含将 Filippov 解的概念扩展到具有不连续右侧和混合时滞的泛函微分方程。利用广义 Halanay 不等式和矩阵测度方法证明了所考虑的 BAM 神经网络的 Filippov 解的全局耗散性。其次，为了实现具有多元不连续激活的 BAM 神经网络的全局指数完全同步，使用泛函微分包含理论和非光滑分析理论以及广义 Lyapunov 泛函方法设计了不连续状态反馈控制器。最后，给出了几个数值例子来证明我们所提出结果的适用性和有效性。
