Adaptive synchronization of the switching stochastic neural networks with time-dependent delays

This paper investigates the synchronization analysis of stochastic neural networks (SNNs) with Markovian switching parameters and time-dependent delays through an adaptive feedback control (AFC) approach. In the process of transmitting signals between neurons, there are unavoidable factors that can degrade the performance of neuronal transmission to list a few, external disturbances, time delays, and parameter uncertainties. Distinct from the existing works on neural network (NN) models, this study focuses on improving the differential model of neural networks (NNs) by considering significant factors such as switching parameters concerning modes, communication time delays during network transmission, and external disturbances. Theoretically, due to these factors, it can be seen that the solution of the differential model can exhibit chaotic behavior that drastically affects the performance of network transmission. In this regard, a synchronization approach is considerably an effective approach for analyzing the dynamic properties of the neuronal model with and without external control input. The relation between the controlled (response) and uncontrolled (drive) neuronal models can be realized through a synchronization approach. On the other hand, the global asymptotical stability of the error model can guarantee the synchronization between uncontrolled-controlled model. In this regard, Lyapunov stability theory and Ito's stochastic calculus can be employed to derive sufficient stability conditions in terms of linear matrix inequalities (LMIs). Numerical simulations are added by choosing a nominal set of parameter values to validate the efficacy of the proposed theoretical frameworks.