Two Researches On Markovian Neural Networks

This article focuses on two classes of Neural Networks.One is Mode-dependent stochastic synchronization criteria for Markovian hybrid neural networks with random coupling strengths,and another is Stability of Markovian jump neural networks with generally incomplete transition probability.Chapter 1 introduces the background of Neural Networks,coupling Neural Networks and Markovian jump neural networks.Chapter 2 is concerned with the stochastic synchronization problem for a class of Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time-delays in the mean square.First,a novel inequality is established which is a double integral form of the Wirtinger-based integral inequality.Next,by employing a novel augmented Lyapunov-Krasovskii functional(LKF)with several mode-dependent matrices,applying the theory of Kronecker product of matrices,Barbalat's Lemma and the auxiliary function-based integral inequalities,several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent Markovian hybrid coupled neural networks.Finally,a numerical example with simulation is provided to illustrate the effectiveness of the presented criteria.Chapter 3,deals with the stability problem for a class of Markovian jump neural networks with mode-dependent delays and generally incomplete transition probability.The delays vary randomly depending on the mode of the networks.Each transition rate can be completely unknown,or only its estimate value is known.By using a new Lyapunov-Krasovskii functional,a delay-dependent stability criterion is presented in terms of linear matrix inequalities(LMIs).