Fixed/predefined-time synchronization of fuzzy neural networks with stochastic perturbations

In this work, fixed-time (FXT) and predefined-time (PDT) synchronization issue of a type of fuzzy cellular neural networks (FCNNs) with stochastic perturbations is concerned via using some improved FXT stability results. First, we introduced some generalized FXT and PTD stability lemmas for a class of nonlinear stochastic differential equation. Then, based on these novel FXT stability results, we investigated the FXT synchronization of a type of FCNNs with stochastic fluctuations by designing two kinds of simple controllers, which not use a linear term −kiei(t) and provide more accurate settling time (ST) estimations compared to early published literatures. Furthermore, we have also analyzed the PDT synchronization of considered stochastic fuzzy networks via developing several nontrivial PDT control protocols and applying some inequality methods. Finally, we provided one numerical example with its Matlab simulations to show the feasibility of our developed results. We believe that methodology used in this paper can provide some new guidance to FXT and PDT synchronization studies of other nonlinear stochastic systems with or without fuzzy templates.