基于忆阻器的随机神经网络的稳定性  

Stability of Stochastic Memristor-based Neural Networks

作　　者：王芬 WANG Fen(School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521

出　　处：《工程数学学报》2022年第4期522-532,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61907010);广东省自然科学基金(2018A0303130120,2017A030313037);广东省教育厅普通高校重点领域专项(2020ZDZX3051)。

摘　　要：与传统的神经网络相比,基于忆阻器的神经网络能够更好地反映突触的强度可变的这一特性,从而更好地模拟人脑的神经系统。在Filippov解的框架下,通过构造恰当的Lyapunov泛函,利用Ito微分公式、微分包含和集值映射理论,研究了一类基于忆阻器的随机神经网络的动力学行为,获得了确保该系统均方指数稳定的充分判别条件。最后,通过给出两个数值仿真的例子验证了结论的有效性。Compared with the traditional neural network, the memristor-based neural networks can better reflect the variable intensity of synapse, so it can better simulate the neural system of human brain. Under the framework of Filippov solution, the dynamical behavior of a class of stochastic memristor-based neural network is studied by employing appropriate Lyapunov functional, Ito’s differential formula, theories of differential inclusions and set-valued maps. Several sufficient conditions are obtained for ensuring the system to be mean square exponential stability in this paper. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

关 键 词：忆阻器 随机 神经网络 稳定性 时滞 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]