Two Researches On Dynamics Analysis Of Neural Networks With Time-varying Delay

This article focuses on dynamics analysis of two classes of Neural Networks with time-varying delay by reciprocally convex approach.One of those is on synchronization for chaotic memristor-based neural networks with time-varying delays,while the other is third-order reciprocally convex approach to stability of fuzzy cellular neural networks under impulsive perturbations.Applying and extending the reciprocally convex approach,combined with Jensen integral inequality,Wirtinger-based integral inequality and other methods,some sufficient stability conditions are obtained.In Chapter 1,the background of Neural Networks,Lyapunov direct method,reciprocally convex combination and the main works of this paper are introduced.In Chapter 2,the synchronization problem for chaotic memristor-based neural networks with time-varying delays is investigated.Firstly,a novel lemma is proposed to deal with the switching jump parameters.Then,a novel inequality which is a multiple integral form of the Wirtinger-based integral inequality is established.Next,several novel delay-dependent conditions are established to achieve the globally asymptotical synchronization for the chaotic memristor-based neural networks by applying the reciprocally convex approach,combined with Briat lemma,auxiliary function-based integral inequalities and a free-matrix-based inequality.Finally,a numerical example is provided to demonstrate the effectiveness of the theoretical results.In Chapter 3,the stability is investigated for a kind of fuzzy cellular neural networks with time-varying under impulsive perturbations.Firstly,the so called third-order reciprocally convex approach to manipulate the new kind of linear combination of positive functions weighted by the inverses of cubic convex parameters is proposed.Then,several novel sufficient conditions to ensure the global asymptotic stability of the equilibrium point of the considered networks are derived by utilizing Briat lemma and third-order reciprocal convex approach.Finally,simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results and lead to wider applications.