Finite-Time Synchronization Study Of Memristor-based Neural Networks

In 1971,Chua first proposed the existence of the fourth basic electrical circuit element and named it as a memristor.Until 2008,Hewlett-Packard Laboratories successfully fabricated the physical model of memristor,then the neural network based on memristive resistance attracts the attention of many scholars due to its unique memory property.In recent years,the synchronization research of memristive neural networks have become a hot topic.However,in the practical engineering process,we are more desirable that the synchronization objective is realized in a finite time,that is,finite time synchronization,finite-time synchronization means the optimality in convergence time.Moreover,the finite-time control techniques have demonstrated better robustness and disturbance rejection properties.In this paper,we study the finite time synchronization of memristive neural networks.This paper uses the theory of differential equations and constructing the appropriate Lyapunov function,designing a suitable feedback controller,using the theory of set-valued map,finite time stability theorem and some inequality technique,theoretical criteria are obtained to ensure finite-time synchronization between drive–response systems under the three different conditions in chapters2–4 of this paper.Finally,we use numerical examples to verify the validity of the obtained theoretical results.