Research On Synchronization Of Chaotic Neural Network With Time-varying Delay

The contemporary world is highly developed in information technology,where plentiful and various information is accessible in any place.However,the problem of information security still lies behind the boom.The secure communication system,especially which is applied in the relevant fields of public security,military and national defense,is directly related to the interest of a nation and its people.Meanwhile,many researchers and users have also paid concern on the security and confidentiality of information transmission and daily telephone contact through the internet.The most important way to strengthen the safety of information transmission is to encrypt it before transmitting;thus,it is crucial to design an encrypted signal which has excellent performance in security and confidentiality.Chaotic signal,with its features of moderate noise,easy concealment,complicated motion trajectory,and complex decrypting process,is best suited for the role of encoded signal.With the rapid development and mutual penetration of neural network and chaos theory,the researchers found that under a certain circumstance,the neural network would become chaotic.Chaotic neural network has a simple structure,which is convenient for hardware circuit designing;its complicated chaotic dynamic behavior can generate a highly complex chaotic signal which has infinite dimension,which can meet the high requirement for encoded signal in secure communication.Thus,it is understandable to use chaotic neural network to encrypt in secure communication.In addition,the information transmission between neurons in the neural network usually has a time delay.The delay would lead the neural network to generate more complicated chaotic time series,increasing the safety factor of the encrypted signal.Besides,chaotic synchronization is used at the receiving end to extract the information before encryption.Because of the introduction of time-varying delay,the design of synchronization controller has become more difficult.In practical engineering,the uncertain parameters of the system will also have a great impact on the performance of synchronous control.The main research work of this paper is as follows:Firstly,a robust synchronization controller is designed for a class of chaotic neural networks with time-varying and parameter uncertainties.The parameter uncertainties are time-varying and norm-bounded.Using stochastic sampling control technique,two random sampling periods with random and given probability are considered.In this paper,a new model with random variables is established,and a new Lyapunov functional is constructed.By using the LIM toolbox of MATLAB,an appropriate controller gain matrix is obtained to guarantee the global mean square robust synchronization of two chaotic neural networks with the same parameters.In addition,compared to the constant sampling,stochastic sampling can get a larger sampling period.Secondly,a class of chaotic neural networks with discrete time delays and distributed delays is considered.Similarly,the controller is designed by using the method of stochastic sampled-data control and input delay.Based on the two sampling periods extend to multi-sampling periods,the synchronization problem of two systems is transformed into the stability problem of the synchronous error state equation with random variables,and reconstructed a new Lyapunov functional.By using inequality technique and free weighting matrix method,we obtain sufficient conditions for global mean square synchronization.The results obtained are better than the same model with Constant sampling period.