Synchronization Analysis Of Fractional-order Time Delay Neural Networks Under Several Different Control Strategies

This paper discusses the synchronization problem of fractional-order time delay neural network under different control strategies.This article uses Lyapunov stability theory,quaternion inequality,extended Cauchy-Schwarz inequality,fractional-order Razumikhin theory and sliding mode control theory etc.to explore the synchronization problem of fractional-order time delay neural networks under three different control strategies,including finite-time synchronization of quaternion time delay neural networks based on self-feedback control techniques,fixed-time synchronization of quaternion time delay neural networks based on adaptive control strategies,and Mittag-Leffler lag projection synchronization of coupled time delay neural networks based on sliding mode control techniques.In the first part,the fixed-time stability theorem for the general differential dynamical system _t0^C D_t^μ＝x（t）（28）f（t,x（t）） is proved by the inverse method and the two-step deflation method,and the maximum settling time of the system is predicted.In the second part,a class of fractional-order quaternion delay neural network systems with finite-time synchronization is discussed.A new type of self-feedback controller is designed based on the self-feedback control technique,and finite-time synchronization criterion for the drive and response system is established by using quaternion direct method,extended Cauchy-Schwarz inequality and quaternion inequality etc.,meanwhile,the rationality of the proposed theory is illustrated by numerical examples.The third part continues with the discussion of the fix-time synchronization problem of the system.A controller with adaptive parameters is designed based on the adaptive control strategy,and the algebraic inequalities for the fixed-time synchronization of the system are derived based on the quaternion theory,the fractional-order Razumikhin theory,the zero-solution stability theory,and so on.Finally,the correctness of the theory is verified by using Matlab tools.In the last part,a variable fractional-order Cohen-Grossberg neural network with coupled delay terms is selected.Based on the defined lag projection error,a new sliding mode controller is designed by using the sliding mode control technique,where some inequality conditions for the Mittag-Leffler lag projection synchronization of the system are derived based on Lyapunov stability theory,sliding mode control theory and some inequality techniques.Finally,the synchronization process is simulated in Matlab toolbox and found to be consistent with the proposed theory.