Predefined-Time (PDT) Synchronization of Impulsive Fuzzy BAM Neural Networks with Stochastic Perturbations

Abstract

This paper focuses on the predefined-time (PDT) synchronization issue of impulsive fuzzy bidirectional associative memory neural networks with stochastic perturbations. Firstly, useful definitions and lemmas are introduced to define the PDT synchronization of the considered system. Next, a novel controller with a discontinuous sign function is designed to ensure the synchronization error converges to zero in the preassigned time. However, the sign function may cause the chattering effect, leading to undesirable results such as the performance degradation of synchronization. Hence, we designed a second novel controller to eliminate this chattering effect. After that, we obtained some sufficient conditions to guarantee the PDT synchronization of the drive–response systems by using the Lyapunov function method. Finally, three numerical simulations are provided to evaluate the validity of the theoretical results.