Stability Analysis of Fractional-Order Hopfield Neural Networks with Time-Varying External Inputs

Fractional-order Hopfield neural networks are frequently utilized to model the information processing of neuronal interactions. It is needed to analyze the stability of such neural systems, when their external inputs are time-varying. In this manuscript, some sufficient conditions are presented firstly for the stability of the non-autonomous fractional-order systems by employing Lyapunov functionals. In further, under time-varying external inputs, fractional-order Hopfield neural networks are regards as a class of non-autonomous fractional-order systems, whose general result is used to acquire the stability conditions of our studied neural system. Moreover, a novel robust synchronization method between such neural systems is proposed with the help of the obtained results. Furthermore, some numerical examples are provided to demonstrate the effectiveness of the presented theoretical results.

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