Synchronization of Fractional Stochastic Neural Networks: An Event Triggered Control Approach

Neural networks (NNs) play a significant role in the machine learning and deep learning domains that include pattern recognition, computer-vision and so on. However, understanding the theoretical properties of neural networks will helps to deliver the user-desired performance in such practical applications. In the literature, the fundamental analysis of a NN, such as stability analysis, parameter sensitivity analysis can be performed by modeling the neuronal activities as differential equations. Through differential equations, the rate at which information is transmitted can be experimented along with various significant factors, such as time-delays during data transmission, switching parameters with respect to time, random disturbances caused by interruption of data blocks. The present study focuses on fundamental analysis of neuronal activities through differential model. Besides, the factors, such as time-delays, exogenous disturbances, and Markovian-jumping parameter (MJP) that has an ability to degrade the stable performance of the neuronal model is incorporated in the model. Distinct to the previous studies in stochastic neural networks, the study address the synchronization problem of stochastic neural networks (SNNs) with fractional-derivative of Brownian motion and event-triggered control scheme. Theoretically, due to nonlinearties, the Lyapunov stability theory is employed to derive the sufficient stability conditions that ensure the stable performance of SNNs. In this regard, looped-Lyapunov functional candidate is considered and corresponding linear matrix inequalitys (LMIs) are derived. Technically, a model of two neurons, three neurons, and four neurons are considered with the given factors to validate the proposed theoretical conditions and controller performance and their results are picturised.