Stability And Synchronization Analysis Of Fractional-order Memristor-based Neural Networks

Fractional-order memristive neural networks have been applied in image processing,associative memories,optimization,automatic control etc.It is a hot topic in the field of mathematics and information science to ensure some dynamical behaviors of the fractional order neural networks.Based on the existing achievements,this paper studies the problem of generalized time stability and boundedness,projective and lag synchronization.The main work including:Firstly,the network synchronization problem is divided into four cases by considering the time varying property of memristor network parameters.By applying the feedback control and adaptive control method,constructed a new adaptive controller and fractional Lyapunov function,an adaptive projective synchronization condition with linear matrix inequalities(LMIs)is established.Secondly,under the frame of fractional Filippov differential inclusion,delayed memristive neural networks are modeled as a fractional-order functional differential equation with discontinuous right-hand.Based on the adaptive control method,the fractional-order adaptive controller is designed to achieve the lag synchronization.Furthermore,the synchronization condition is proposed in the form of linear matrix inequalities.Finally,the existence and uniqueness of the equilibrium point of fractional order memristive neural networks is proved by topological degree theory.Under the frame of fractional Filippov differential inclusion,the definitions of the generalized finite time stability and boundedness of the equilibrium points of fractional order systems are given.Using the generalized Gronwall inequality and the Laplace transform,the sufficient conditions to guarantee the generalized finite-time stability and boundedness for the systems are established in terms of linear matrix inequalities.