The Global Stability And Synchronization Of The Cellular Neural Networks With Delays

The cellular neural network with delays is a large-scale nonlinear dynamic system. It has a widely applying in many fields, such as pattern recognition, signal processing, automatic, associative memories. As a dynamic system, all kinds of static models presented by neural system are the basis of a series of intelligent activities, such as the simulative study of biological neural system, the associative memories and the pattern recognition. Its stability is very important in dynamic systems. Therefore, the study of cellular neural networks with delays has an important meaning in theory and practice.In the first chapter, the development and history of neural networks are discussed, the current status in delayed cellular neural networks, stochastic cellular networks and synchronization of cellular neural networks have been introduced.In the second chapter, the global exponential stability of equilibrium point of a class of stochastic fuzzy cellular networks with time-varying delays is proposed. By constructing proper Lyapunov functional and using the Ito differential formula and inequality technique, delay-independent and delay-dependent sufficient conditions for the global exponential stability are obtained.In the third chapter, the asymptotic stability in distribution of stochastic cellular neural networks with time delays and Markovian switching are investigated. By constructing Lyapunov functional, some sufficient conditions for the asymptotic stability in distribution of stochastic cellular neural networks with time delays and Markovian switching are obtained.In the fourth chapter, the global exponential stability a class of cellular networks with multi-proportional delays is studied. The sufficient conditions of existence and uniqueness of the equilibrium of the system were obtained by constructing suitable Lyapunov functional.In the fifth chapter, the global asymptotic synchronization of equilibrium point of a class of cellular networks with time-varying delays is study. By constructing suitable Lyapunov functional and using the inequality technique, the sufficient conditions for the global asymptotic synchronization of the derive-response structure of cellular networks are obtained.In the thesis, all the obtained conclusions are new, and we give numerical examples and simulations to show the effectiveness of the results.