Stability Of Fuzzy Cellular Neural Networks With Reaction-Diffusion Terms

In this paper, we study the stability of fuzzy neural networks with delays and reaction-diffusion terms. By constructing suitable Lyapunov functionals, using the analytical method based on differential inequality, utilizing Ito differential formula, and some other inequality techniques, we obtain some sufficient conditions for the exponential stability of the solutions for fuzzy neural networks with delays and reaction-diffusion terms. The results impose constraint conditions on the network parameters independently of the delay parameters. The results are also easy to check and play an important role in the design and application of exponentially stable fuzzy neural circuits.The organization of this paper is as follows:In the first chapter of this dissertation, we reviewed the development of fuzzy cellular neural networks. The importance of studying the stability of fuzzy cellular neural networks with delays and reaction-diffusion terms is explained. Also the current status in such area is introduced.In the second chapter, we study global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional, using Hanalay inequality, we obtain sufficient conditions for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy neural networks with delays and reaction-diffusion terms, respectively.In the third chapter, we study global exponential stability of fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional, using differential inequality, we obtain sufficient conditions for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy neural networks with distributed delays and reaction-diffusion terms, respectively.In the fourth chapter, we study mean square exponential stability of stochastic fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional, using Hanalay inequality, and utilizing Ito differential formula, we obtain sufficient conditions for the mean square exponential stability of the solution for a class of stochastic fuzzy neural networks with delays and reaction diffusion terms, respectively. In the fifth chapter, we study mean square exponential stability of stochastic fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional, using differential inequality, and utilizing Ito differential formula, we obtain sufficient conditions for the mean square exponential stability of the solution for a class of stochastic fuzzy neural networks with distributed delays and reaction diffusion terms, respectively.In the sixth chapter, the research work of this paper is summarized, and the future developing directions are included.