With Unknown Transition Probability And A Bam Neural Networks With Mixed Delay Stability Analysis And Synchronization

Stochastic bi-directional associative memory BAM neural networks is a new interdiscipline, and in recent years it caused extensive research and great progress has been achieved in this subject. This paper studies the stochastic stability and mean-square global gradual synchronization issues of a BAM neural network with a mixed time-delay and unknown transition probability. Consider that the BAM neural network model contains both discrete and infinite distributed delays, and its system contains a Markov process. In the paper, we acquire the qualification of the stochastic stability and the global gradual synchronous analysis in consideration of mean-square. The result can be impressed into the form of LMI, So the problems can be resolved through the mathematic soft, just like Matlab LMI Toolbox. Finally, we make two numerical simulation to illuminate the validity and application.In this paper, Finally, two numerical examples are given to illustrate the effectiveness and applicability of the proposed theory in this paper. It is worth pointing out that many existing results are special circumstances and all of them are included in our analysis.The whole text consists of three parts:In the first part, we not only introduce the background and significance of studying the BAM neural network which contains a mixed time-delay, but also summarize the development of dynamics in the BAM neural network with a mixed time-delay. The main introduction of my study has been shown in this part as well.In the second part, we begin with introducing the model of BAM neural network and related assumptions, we firstly construct a new Lyapunov-Krasovskii function. Then some techniques are adopted to make the system node’s random stability analysis. The results of these analyses would be expressed in the forms of the linear matrix inequality (LMI), which can be solved effectively by the mathematic software such as Matlab LMI ToolboxIn the third part, we study the BAM neural network of mean square synchronization problem. We adopt Lyapunov theory and Kronec ker products of matrix to obtain the synchronization analysis. And numerical example is given to illustrate the effectiveness of the presented method.