School of Financial Mathematics & Statistics, Guangdong University of Finance, Guangzhou 510521, China.
School of Financial Mathematics & Statistics, Guangdong University of Finance, Guangzhou 510521, China.
Neural Netw. 2018 Feb;98:192-202. doi: 10.1016/j.neunet.2017.11.007. Epub 2017 Nov 24.
Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô's differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy-Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results.
基于随机忆阻器的双向联想记忆（BAM）神经网络具有时滞，在神经网络系统的设计和实现中起着越来越重要的作用。在 Filippov 解的框架下，研究了基于随机忆阻器的 BAM 神经网络的 p 阶矩指数稳定性问题。利用随机稳定性理论、Itô 微分公式和 Young 不等式，得到了判据。同时，利用 Lyapunov 方法和 Cauchy-Schwarz 不等式，得到了上述系统均方指数稳定性的充分条件。所得结果改进和扩展了基于忆阻器或常规神经网络动力系统的已有研究成果。给出了四个数值实例来说明所提出结果的有效性。
