Analysis On Synchronization And Stability Of Stochastic Complex Dynamical Networks

In this dissertation, rigorous mathematical analysis is carried out for the synchro-nization behavior and robust stability of some stochastic complex networks models. For all possible random perturbations, randomly occurred nonlinearities, some dif-ferent types of time-delay phenomena, parameter uncertainties as well as Markovian switching parameters involved in the proposed models, the analysis problems are investigated by utilizing the'delay-fractioning'approach, and then the criteria of stochastic synchronization stability or robust stability are derived in terms of linear ma-trix inequalities(LMIs). Moreover, based on the obtained sufficient conditions, both the theoretical analysis and numerical simulation verify the feasibility and superiority for the developed results.This dissertation is divided into seven chapters.Chapter 1 is for exordium. This chapter summarizes the research significance and related background knowledge. Also, the research problems and the main con-tent, as well as the contribution of this thesis are listed in detail.In the 2nd Chapter, we deal with the stochastic synchrony analysis problem for a class of stochastic continuous-time complex networks with constant time-delay and random perturbations. By utilizing the properties of matrix Kronecker product, stoch-astic analysis theory, free-weighting matrix method and LMI techniques, the criteria are derived to ensure the synchrony stability for the addressed networks. A numeri-cal simulation example indicates that the main results with less conservative and the conservatism could be reduced further as the number of fractioning gets bigger.In Chapter 3, the stochastic synchrony stabilization problem for a novel array of coupled continuous-time stochastic complex networks with randomly occurred non-linearities, interval time-varying delays, unbounded distributed time-delays as well as multiple random perturbations is investigated. The stochastic nonlinearities is de-scribed by using random variables with Bernoulli distributed sequence and the sector-like nonlinear functions.In Chapter 4, the global synchronization problem is addressed for a new array of coupled stochastic complex dynamical networks in discrete-time domain with mixed time-delays, stochastic nonlinearity and stochastic disturbances. The integral-type distributed time-delays in the discrete-time domain system is described by using the infinite series method. By combining with the Lyapunov-like matrix functional, free-weighting method and matrix Schur complement approach, as well as the stochas-tic analysis theory, several sufficient conditions are obtained to grantee the global asymptotic synchronization in the mean square sense for the discrete-time stochastic delayed complex networks.In Chapter 5, the robust stabilization problems are considered for a class of un-certain delayed genetic regulatory networks with or without stochastic disturbances. By using the'delay-fractioning'method and Lyapunov stability theory, sufficient conditions are obtained to ensure the robust stability or robust stochastic stability for the proposed networks models. Two different time-delays, respectively, exist in the translation process and the regulatory feedback process, where the feedback regula-tion is described by a sector-like nonlinear functions.Chapter 6 is concerned with the stochastic synchrony analysis problem for a gen-eral class of stochastic genetic oscillator networks with both time-delays and Marko-vian jumping parameters. The nodes indicate the biochemicals and the couplings rep-resents the biochemical interactions. The regulatory functions of the addressed ge- netic oscillator networks are of the sector-like nonlinear function form. By utilizing the up-to-date time-delays analysis approach, a novel matrix functional is formulated to derive the synchronization conditions for the addressed networks.In Chapter 7, we summarize the main results of the thesis, and discuss the re-search work in the future.