Semi-global synchronization of stochastic mixed time-delay systems with Lévy Noise under aperiodic intermittent delayed sampled-data control

This article studies the semi-globally exponential synchronization of stochastic mixed time-delay systems with Lévy noise (SMTDSLN) under aperiodic intermittent delayed sampled-data control (AIDSC). Thereinto, a new aperiodic intermittent sampled-data control, which is aperiodically intermittent and samples at a past interval but not a moment, is proposed. Secondly, considering the coupling factor, we utilize the vertex Lyapunov–Krasovskii (L–K) functional and combine the graph theory method to construct the global L–K functional and give its properties. This construction method is introduced for the first time in studying the semi-globally exponential synchronization of SMTDSLN. Next, combined with Halanay inequality, sufficient conditions for semi-global synchronization of SMTDSLN under AIDSC are given, including estimations of the non-control rate and the relationship between the initial condition range and AIDSC. Finally, we apply these results to bidirectional associative memory neural networks (BAMNNs) and give two corresponding numerical examples to demonstrate the validity of the theoretical results.