Stability And Synchronization For Several Types Of Delay Systems

Delay neural networks are a part of delay system and they are frequently encounteredin various areas such as signal processing, pattern recognition and combinational optimiza-tion. Thus dynamic problems of delay neural networks have received considerable attention bymany researchers, especially the stability and dissipativity. On other hand, synchronization ofcomplex networks is a common phenomena in nature and engineering ?eld. The topologicalstructures of complex networks are important to dynamic network synchronization. The mainobjective of this dissertation is to investigate stability of delay neural networks and synchro-nization of complex networks in di?erent topological structures.The main content and contributions of this dissertation are summarized as follows:1. The stability problem of stochastic delay neural networks with Markovian jumping pa-rameters is discussed by utilizing delay-dividing approach combined with Lyapunov-Krasovskiifunctional and Ito? formula. Some improved delay-dependent stochastic stability criteria androbust stochastic stability are obtained. Meanwhile, the stability of stochastic delay BAM neu-ral networks and uncertain stochastic delay BAM neural networks are investigated by utilizingfree weighing matrices. Fuethermore, the global output convergence problem of neural networkswith time-varying and distributed delays is proposed by using M-matrices theory.2. The global dissipativity problem of neural networks with time-varying and distributeddelays is investigated by using Lyapunov function and Lyapunov-Krasovskii functional respec-tively. And some attractive sets are obtained. Morreover, the existence and global attractivityproblem of a unique almost periodic sequence solution for a class of discrete-time neural net-works with delays are denoted.3. The synchronization problem of competitive neural networks with di?erent time scalesis studied by utilizing delay-dividing approach. By dividing the whole delay interval into twosegments such that some synchronization condition are derived even if the derivative of delay isnot di?erential or unknown. Numerical simulations are shown to demonstrate the e?ectivenessof the obtained results.4. The exponential synchronization problem of complex networks with delayed and nonlin-early nodes is discussed by designing feedback controller. Meanwhile, the outer synchronizationof complex networks is between two complex dynamical networks with di?erent topologies anddiverse node dynamics. Finally, the synchronization of delayed discrete-time complex networksis studied by utilizing free matrices. Numerical simulations are shown to demonstrate the ef-fectiveness and less conservativeness of the proposed results.