Containing The Reaction Diffusion Varying Delay Cohen-grossberg Neural Network Stability Analysis

Neural networks play an important role in signal and dynamic image processing, artificial intelligence and optimization. Recently, more and more attentions have been paid to the study of the dynamics of neural networks. The researches on neural networks for stability of equilibrium and periodic solution have been deepened (including asymptotic stability, exponential stability, robust exponential stability, absolute stability, periodic stability, and so on), and a series of significant results have been obtained. In the study of stability, there are many expression forms about stability results, such as M (P or H)-matrix, matrix measure, matrix norm, linear matrix inequalities, algebraic inequalities and so on.In this paper, we investigate the stability analysis problems for a class of reaction-diffusion Cohen-Grossberg neural network with variable delay. At first, we give the new conditions for global exponential stability and use matrix theory, algebraic inequalities and the basic concept of the stability to prove the global exponential stability of the given model. Besides, we use an example to show that our conditions and results are more universal and practical. Then, we use homotopy mapping theory, topological theory and M -matrix theory to prove the existence, uniqueness and global robust exponential stability of the given model. The model studied in this paper including Cellular neural networks, Hopfield neural networks, and general Cohen-Grossberg neural networks. So, all conditions and results are also applicable to judging the stability of these models. Moreover, this paper is also extending the results of reaction-diffusion Hopfield neural network with variable delay that studied by wang Ls, the model of [76],the model that studied by Liao XX, and reaction-diffusion Cohen-Grossberg neural network with variable delay that studied by Wu BH, conditions and results can be obtained by simplifying some counter-parameters. The model, conditions and results are more universal and practical than former papers.