Dynamical Analysis And Control Of Memristive Neural Network

Memristor is a kind of non-linear resistor with memory function,which has the advantages of small size,low energy consumption,fast reading and writing speed and it is considered to be an ideal component for simulating human brain to realize artificial intelligence.The emergence of memristor provides a good research direction for the speed contradiction between computation and storage and owns important theoretical and engineering significance.Memristive neural networks is built by using memristor instead of resistance in neural network.Because of the special properties of memristor,the research results of neural network system can not be directly applied to memristive neural network system,and the research on the dynamic behavior of memristive neural network system is still in the early stage.Therefore,this paper focuses on the dynamical behavior theory of memristive system.In the framework of Filippov solution,different dynamical behaviors and control of memristive system are studied by using differential inclusion theory and convex hull theory etc.All the following theoretical results are verified by simulation.The work of this paper as follows:(1)The stability of complex-valued memristive neural network system with delay is studied.According to Liouviille's theorem,there is no bounded and analytical activation function in the complex value domain.The complex-valued memristive neural network system is divided into two real-valued systems for analysis.By using the knowledge of Mmatrix,it is proved that the two real-valued memristive systems obtained after the split are an isomorphism of the original complex-valued memristive system.Based on the proof of isomorphism and the Lyapunov stability theory,using the knowledge of M-matrix again,the stability of the original complexvalued system is indirectly proved by proving the stability of the two real-valued systems obtained after the split.(2)The synchronization problem of complex-valued memristive delayed neural network system via periodically intermittent control is studied.Under control of periodically intermittent controller,and by using the relevant theory including Hanalay inequality,sufficient conditions related to the control period and delay are obtained.In addition,based on aperiodically intermittent strategy,finite-time synchronization of memristive neural network system with time-varying delays and parameter uncertainties is studied.By designing appropriate aperiodically intermittent adjustment controller,sufficient conditions and finite-time are derived T.The research shows that the designed aperiodically intermittent adjustment controller can effectively eliminate the parameter uncertainties caused by external disturbances and achieve finite-time synchronization.(3)Quasi-projective synchronization problem of complex-valued memristive neural network system with switching jumps mismatch is studied.Under the framework of differential inclusion,in order to deal with switching jumps mismatch that caused by removing common constraints of activation function,and a lemma related to the switching threshold and the projective scale factor are derived.Under the control of the linear feedback controller,by using the derived Lipschiz conditions and the related theory of quasi-projective synchronization with and without delays,the quasi-projective synchronization criteria with and error bounds without delays under switching jumps mismatch are derived.(4)The problem of quasi-synchronization of fractional-order complex-valued memristive neural network systems under switching jumps mismatch is studied.Based on the fractional differential inclusion theory,under the definition of the Caputo(? ?(0,1))fractional derivative,the relevant quasi-synchronous theory with no delay and delay and the properties of the Mittag-Leffler function under this definition are applied.By using linear feedback controller,the quasi-synchronization problems of this type of fractional-order complex-valued neural network system with delays and without delays are discussed respectively,and the corresponding quasisynchronization criteria and error bounds are derived.