Mean Square Asymptotic Stability of Discrete-Time Fractional Order Stochastic Neural Networks with Multiple Time-Varying Delays

In this paper, the mean square locally and globally asymptotic stability problem of discrete-time fractional order stochastic neural networks(DFOSNNs) with multiple time-varying delays are investigated. Firstly, the DFOSNNs model with multiple time-varying delays are established. Then, the general framework for the mixed delays Halanay-type inequality has been established with no harsh assumption. Further, the locally and globally asymptotic stability of DFOSNNs with multiple time-varying delays in mean square sense are proved via Halanay-type inequality respectively. In addition, the sufficient condition for globally asymptotic stability of DFOSNNs with multiple time-varying delays in mean square sense is derived via Lyapunov–Krasovskii functional method. From the results obtained in this paper, the two theorems of global asymptotic stability are complement each other. Finally, three numerical examples are given to show the validity of the obtained theoretical results.