Stability And Synchronization Of Fuzzy Neural Network With Mixed Delays

Artificial neural networks simulate the neural system of biological in the informationprocessing, which is different from the traditional mode of information processing. As a result, theartificial neural networks have been widely used in various fields, such as diagnosing the problem,medicine, commercial, financial industry, robot control, signal processing, computer vision and soon. Fuzzy neural networks have the advantages of both fuzzy logic and neural network, whichreceive the attention of more and more researchers. In this thesis, the stability of fuzzy neuralnetwork with time-delays is analyzed, and the synchronization control problem is investigated forthe drive and response systems with different driving function. Finally, the synchronization controltheory has been realized in the application of secure communication.In chapter one, the background of neural networks and their synchronization are introduced,and the main innovations of this thesis are highlighted. In chapter two, the preliminary of this thesisis given, including the definition, related lemma and related symbols. In chapter three, theexponential stability of fuzzy neural networks with distributed delays is studied based on theexisting research results. The suitable Lyapunov functions are constructed on the basis of Matrixtheory and fix-point theory. It is proved that the only equilibrium point exists and it is asymptoticallystable in the system, and some sufficient conditions of stability are given. In chapter four, thesynchronization problem of fuzzy cellular neural network with non-identical mixed delays is studied.The stability of error system is discussed by using the sliding mode control of the state feedback tothe uniformly synchronization, and the sufficient condition is given for the uniformlysynchronization. The simulation results corroborate the effectiveness and feasibility of the slidingmode control. In chapter five, based on the model of system in the chapter four, the synchronizationcontrol of non-identical fuzzy cellular neural networks is applied to secure communication in atwo-dimensional model system. The useful message is loaded on the chaotic signal and the usefulinformation is recovered in the receiving terminal, where the encryption and decryption processingof the useful signal is realized by synchronization control.