Passivity Analysis Of Delayed Neural Networks With Reaction-diffusion Terms

Neural networks are mathematical models to simulate behavior mechanisms of the brain for information processing.Due to its highly nonlinear characteristics and circuit realizability,neural networks are widely used in practical problems such as pattern recognition,combinatorial optimization,and associative memory.As a prerequisite for the application of neural network model,its dynamic behaviors have been extensively studied,including the inherent dynamic characteries such as passive,stability.Passivity originates from the branch of electrical network theory and physics.and its essential feature is to maintain the stability of the system,which has been widely used in the field of circuit system,physics,mechanics,applied mathematics and so on.This dissertation mainly studies the passivity problem of neural networks,and analyzes the influence of time-varying delays,distributed delays and diffusion effect on the passivity of neural networks.The main results of this dissertation are as follows.First,the passivity of memristor-based delayed neural networks with reactiondiffusion terms is investigated.For a class of memristor-based delayed neural networks with reaction-diffusion terms,the passive,output strict passivtity and input strict passivity of the proposed model with time-varying delays and without any delay are analyzed by making full use of Lyapunov functional and inequality techniques.The obtained criteria consider the sign difference of the elements in connection matrices,for which they represent the inhibitory and excitatory effects of the neural networks,thus they overcomes the shortcomings of the results based on M-matrix and algebraic inequality.Finally,the memristor-based delayed neural networks with reaction-diffusion terms is applied to pseudo-random number generation,and the encrypted signals which are obviously different from the original signals are obtained?Second,the passivity of coupled neural networks with reaction-diffusion terms and mix delays is studied..A class of coupled reaction-diffusion neural network models with time-varying delays and distributed delays is proposed.By constructing appropriate Lyapunov functional,with the virtue of Green formula,Jensen inequality and Schur complement lemma,several criteria are obtained in the form of linear matrix inequalities,which can be used to ascertain the passivity,output and input strict passivity of the proposed system.And the obtained results extend and improve the existing conlusion.Finally,we reveal the realtionship between passivity and stability.