| The concept of memristor was proposed by Professor Chua in 1971,while the real prototype of memristor was first developed by HP Labs in 2008.The memristor-based neural networks are formed by combining the memristor with the artificial neural networks,which are widely used in combination optimization,pattern recognition,image protection and other fields.Both integer-order and fractional-order memristor-based neural networks have complex dynamic characteristics,and synchronization as an important dynamic behavior has been widely concerned.In addition,the signal transmission is not instantaneous but with delay,and the existence of delay will reduce the stability of the system and even.Therefore,the influence of time delay on synchronization can not be ignored.Compared with asymptotic or exponential synchronization,finite-time and fixed-time synchronization can ensure faster convergence of errors and better meet the actual needs,which have important research significance,which are of great research significance.Based on the above reasons,this paper studies the finite and fixed-time synchronization of fractional-order and integer-order delayed memristor-based neural networks by designing effective control schemes.The main work arrangements are as follows:Firstly,the finite-time synchronization of fractional-order delayed memristor-based neural networks is studied.Considering the influence of leakage delay and uncertainty on synchronization,an adaptive sliding mode control algorithm is proposed to realize the estimation of unknown upper bound disturbance.Further combining with finite-time synchronization theory,corresponding synchronization criteria and explicit expression of the settling time are obtained.Based on relevant knowledge of secure communication,the obtained results are applied to the encryption and decryption of plaintext signals.The effectiveness of the proposed method is verified by numerical simulation and secure communication application.Secondly,the fixed-time synchronization of delayed memristor-based neural networks is studied.The effect of mixed time delays on synchronization is considered.The right-hand discontinuity of memristor and discontinuous activation functions is treated by using set-valued mapping and differential inclusion theory.The feedback control and adaptive control strategies are designed to eliminate the influence of mixed time delays on synchronization.Based on fixed-time synchronization theory,the synchronization criteria for continuous and discontinuous activation functions and the settling time expressions independent of initial values are obtained respectively.The simulation platform is built to verify the feasibility of the proposed method.Finally,the fixed-time synchronization of stochastic memristor-based neural networks is studied.Considering the influence of mixed time delays and external stochastic disturbance,an adaptive control scheme is proposed to realize tracking estimation of unknown parameters.The fixed-time synchronization criteria are obtained by using stochastic Lyapunov theory and comparison theorem,and the upper bound expression of synchronization time is derived.At the same time,the criterion conditions of finite-time synchronization under the same model are also given.The feasibility of the theoretical results is verified by the simulation platform. |
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