Synchronisation analysis for fractional-order discrete-time high-order BAM neural networks with time-varying delays

This paper investigates the problem of quasi-synchronisation (QS) and complete synchronisation (CS) for a class of fractional-order discrete-time high-order bidirectional associative memory neural networks (DFBHONNs) with time-varying delays. Firstly, by employing the Caputo fractional difference operator, the Mittag–Leffler function, and the Laplace transform, two Caputo fractional difference inequalities are established. Secondly, based on the proposed inequalities and several analytical techniques, new sufficient conditions are derived to guarantee QS under a hybrid controller and CS under an adaptive hybrid controller for the considered DFBHONNs. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.