Research On Finite-time Projection Synchronization Of Two Fractional-order Neural Network Models With Delay

Fractional order calculus generalizes the order of integral order calculus from inte-gers to real numbers.Compared with the traditional integer order calculus,fractional order calculus can better describe the dynamic behavior of the system.Therefore,it will be more promising to introduce fractional order theory into neural network.In recent decades,fractional order neural network has been widely concerned because of its ap-plication in many fields.In this paper,we consider the finite-time projective synchro-nization problem for two classes of fractional neural networks with delay.One is the fractional order fuzzy neural network with mixed delay,the other is the discontinuous fractional-order neural networks with time-varying delays.Firstly,the finite-time projective synchronization problem of fractional order fuzzy neural networks with mixed delays is studied.In this part,we discuss the finite-time projective synchronization problem of the system in the case of 0<r ?1/2 and 1/2<r<1.The sufficient conditions for the finite-time projective synchronization of the neural network system are obtained by means of Gronwall inequality,Cauchy-Schwartz inequality and other inequality skills.Secondly,the finite-time Mittag-Leffler projective synchronization of discontinuous fractional-order neural networks with time-varying delays is discussed.The solution of master-slave system in the sense of Filippov is obtained by using the differential inclusion theory.And then,by constructing the Lyapunov function and inequality skill,the sufficient conditions of the finite-time Mittag-Leffler projective synchronization of the neural network system are obtained via a suitable controller.In addition,the projective synchronization of master-slave ystems under another controller is studied by using the inequality skill.