Fixed-Time Synchronization of Memristor-Based Stochastic BAM Neural Networks with Time-Varying Delays

This paper considers the fixed-time synchronization of memristor-based bidirectional associative memory neural networks with stochastic perturbations and time-varying delays via designing concise function based continuous controllers. First, under the Filippov set-valued mapping framework, the discontinuous stochastic memristor-based bidirectional associative memory neural networks model is transformed to stochastic differential inclusion. Then, two innovative controllers are designed to achieve fixed-time synchronization for the system: a nonlinear state feedback controller without linear terms, which significantly simplifies the design complexity, and an adaptive control scheme with an efficient update law, which automatically adjusts coupling strength of the control gain to save overall control cost. Furthermore, some sufficient criteria for the fixed-time synchronization in probability of considered system are established by using improved fixed-time stability results and some inequality techniques. Finally, the effectiveness of established theoretical results is demonstrated through two numerical examples.