On The Dynamics Of Neural Networks Models With Reaction-diffusion Terms

Since neural networks have enormous potential in wide varieties of applications, manyspecialists and scholars apply themselves to the research of the theory and achieve manyperfect productions. In this paper, we perform researches of dynamical behaviors of threeclasses of neural networks model with reaction-di?usion terms. The main contents of thispaper include: the exponential stability analysis for a class of impulsive Cohen-Grossbergneural networks with delays and reaction-diffusion; the boundedness, invariant sets andexponential stability for a class of non-autonomous Cohen-Grossberg neural networks withdiscrete delays and reaction-diffusion terms respectively; the attracting and invariant setsand the exponential stability for a class of impulsive fuzzy cellular neural networks withdelays and reaction-di?usion terms.The main contents in this paper can be summarized as follows:1. Firstly, in the first section of the first chapter, we introduce the developmentalprocess and significance of neural networks. In the following section 2 we introduce themodels of neural networks and some results for neural networks, in with Cohen-Grossbergneural networks and fuzzy cellular neural networks be introduce specially. In section 3,we introduce the research results for neural networks with reaction-diffusion terms. Insection 4, the organization of this paper is given.2. In the second chapter, we investigate a class of impulsive Cohen-Grossberg neuralnetworks with distributed delays and reaction-diffusion. Under the assumption that thereare equilibrium points of system, a series of suffcient conditions is obtained for checkingthe uniqueness and global exponential stability of a class of impulsive Cohen-Grossbergneural networks with delays and reaction-diffusion by using inequality techniques andgeneral Lyapunov functional. Finally, we give a example to illustrate the effciency of ourresults. In this chapter, the forms of impulsion of model are general and are not linear.3. In the third chapter, a class of non-autonomous Cohen-Grossberg neural networkswith discrete delays and reaction-di?usion terms is discussed. Firstly, we research the the boundedness and the invariant sets by applying M-matrix and the constant variation.Then, some suffcient conditions on the global exponential stability are established byconstructing a suitable Lyapunov function. Finally, we give twe examples to illustrate thee?ciency of our results.4. In the forth chapter, the dynamical behaviors of a class of impulsive fuzzy cellularneural networks with delays and reaction-diffusion terms are studied. Under the assump-tion that there is an unique equilibrium point of system, some suffcient conditions on theglobal exponential stability of equilibrium point are established and the the attractingsets and invariant sets are obtained by applying general Halanay inequality. Finally, aexample is given to illustrate the e?ciency of our results.