Font Size: a A A

Stability And Chaos Synchronization Of Delayed Neural Networks

Posted on:2006-11-29Degree:DoctorType:Dissertation
Country:ChinaCandidate:C D LiFull Text:PDF
GTID:1118360155472586Subject:Computer software and theory
Abstract/Summary:PDF Full Text Request
The delayed neural networks exhibiting the rich and colorful dynamical behaviors are an important part of the delayed large systems. Due to their important applications in signal processing, image processing as well as optimizing problems, the dynamical issues of delayed neural networks have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums and/or periodic solutions of delayed neural networks have been derived via Lyapunov-type function/functional approaches. In addition, the bifurcation and chaos in delayed neural networks have also been investigated intensively, and a series of significative results have been obtained. This thesis mainly focuses on the global stability for two types of delayed neural networks and chaotic synchronization of coupled neural models with chaos. Specifically, the main contents are as follows: 1. Stability analysis for Hopfield neural network models with time-varying delays The stability issue of the equilibrium point of Hopfield neural networks has attracted much attention and a lot of relevant results have been reported in the open literature. In this thesis, a novel asymptotical stability criterion with less restriction is derived via transforming the original model into an equivalent descriptor system. 2. Stability analysis for BAM neural network models with multiple delays Some novel and easily verified sufficient conditions for global exponential stability of BAM neural networks are established via constructing an appropriate Lyapunov-Krasovskii functional, and furthermore, the exponential convergence degrees of the stable BAM models are discussed in detail. 3. Robust stability analysis for interval neural networks with delays Based on the analysis on the recent results reported in the literature, an improved robust stability criterion is derived with the help of a new matrix inequality proposed by this author. Furthermore, a new analytic approach for stability issues of interval systems is exploited by employing the equivalence of the sets of interval matrices. Applying this new approach to the generalized Hopfield neural networks yields a set of novel robust stability results. 4. Linear feedback based chaos lag-synchronization of delayed neural networks The theoretical analysis for chaos lag-synchronization in linearly coupled chaotic systems with time delays is made, which explains some of the recent observations in both circuit and laser experiments. In addition, the speed of the transition to lag-synchronization is also discussed. 5. Chaos control and synchronization via impulsive control approach Duo to the complexity and imperfection of impulsive control theory for delayed systems, to the best of the author's knowledge, chaos synchronization of delayed systems via impulsive control approach has few (if any) results. In this sense, the presented work may be innovative, which lead to potential application in secure communication. 6. Hybrid synchronization in coupled chaotic neural systems A new observation, i.e., hybrid synchronization in coupled chaotic neural systems, is reported for the first time, to the best of the author's knowledge. As an example, this phenomenon is demonstrated by 3-D Chen system with simple linear feedback.
Keywords/Search Tags:Neural networks, Time delay, Stability, Lyapunov-Krasovskii functional, Chaos, Lag synchronization, Impulsive control, Linear matrix inequality (LMI)
PDF Full Text Request
Related items