Mean-Square Stability Analysis of Fractional-Order Time-Delayed Neural Networks Driven by Fractional Brownian Motion

This paper mainly investigates the stability of fractional-order time-delayed neural networks (FOTDNNs) driven by fractional Brownian motion. In particular, it examines the mean-square uniform stability of FOTDNNs with the Hurst parameters 12<H<1. By applying the Cauchy-Schwarz inequality and analytical techniques, we establish sufficient conditions that guarantee mean-square uniform stability and further derive the stability criteria for systems with H=12. The validity of the theoretical results is confirmed through two numerical examples. Finally, we analyze the influence of the Hurst parameter (12⩽H⩽1) and key parameters of the sufficient conditions on FOTDNNs.