基于忆阻器的随机神经网络的稳定性

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 It$hat{rm o}$ 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。

Stability of Stochastic Memristor-based Neural Networks

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, It$hat{rm o}$'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.