Researches On Synchronization Problems Of Markovian Complex Neural Networks With Time-Varying Delays

Many systems in nature can be described as complex networks.Such systems include biological neural networks,power grids,communication networks,WWW,metabolic systems and so on.Complex networks that are composed of a large num-ber of highly interconnected dynamical nodes(individuals)have attracted more and more attentions from various fields of science and engineering.Hence,the research of the complex networks has become a important research topic in the field of com-plexity science.Synchronization phenomenon,as a typical collective behavior and one of the most important dynamic properties of complex networks,is widespread in all kinds of complex network systems.The synchronization of complex networks has great application potential in secure communications,network congestion con-trol,multi-agent consensus and other fields.In order to better understand the synchronization behavior of complex networks and utilize useful synchronization to avoid harmful synchronization,it is very important to study the synchronization of complex networks.The complex networks system often experiences abrupt changes in their struc-ture and parameters due to phenomena such as component failures or repairs and sudden environmental disturbances.In order to reflect more realistic dynamical be-haviors,synchronization problems of Markovian complex networks have attracted more and more attention.This dissertation studies stochastic synchronization,lo-cal synchronization control,sampled-data synchronization and finite-time synchro-nization of Markovian complex neural networks with time-varying delay,and the corresponding less conservative synchronization criteria are proposed.Numerical simulations are given to illustrate the effectiveness of the theoretical results.The main contents and contributions are listed as follows:(1)The synchronization problem of Markovian coupled neural networks with par-tial information on transition probabilities and random coupling strengths is investigated.The coupling strengths are mutually independent random vari-able in this system.By designing a novel augmented Lyapunov-Krasovskii functional and using reciprocally convex combination technique and the prop-erties of random variables,new delay-dependent synchronization criteria are proposed.The obtained criteria depend not only on upper and lower bound-s of delay but also on mathematical expectations and variances of random coupling strengths.(2)Since some systems contain information about the derivative of the past state,the local synchronization of Markovian coupled neutral-type neural networks with partial information on transition probabilities is investigated in the first time.The coupling configuration matrices are not restricted to be symmetric.By designing an augmented Lyapunov-Krasovskii functional and applying a special coupling configuration matrix,the new delay-dependent local synchro-nization criteria are proposed.(3)The local synchronization of Markovian nonlinear coupled neural networks with uncertain and partially unknown transition rates is investigated.Each transition rate in Markovian process is uncertain or completely unknown be-cause of the difficulty and high cost in obtaining the complete knowledge of the transition rates.By applying the novel Lyapunov-Krasovskii functional,and a new integral inequality combined with free-matrix-based integral inequal-ity and further improved integral inequality,the new less conservative local synchronization criteria are proposed.(4)The less conservative sampled-data synchronization conditions of Markovian coupled neural networks with mode-dependent time-varying delays and ape-riodic sampling intervals are proposed.By applying a novel mode-dependent augmented Lyapunov-Krasovskii functional,an extended Jensen's integral in-equality and Wirtinger's inequality,new delay-dependent synchronization cri-teria are obtained,which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay.In addition,the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities.(5)The new switching Markovian coupled neural networks model is established,and the finite-time synchronization criteria of this system is proposed in the first time by using the novel stochastic multiple Lyapunov-Krasovskii func-tional and a new less conservative weighted integral inequality.This coupled neural networks consist of a higher level switching and a lower level Marko-vian jumping,and the time-varying delays in this system depend on not only switching signal but also jumping mode.Hence,this new model is more gen-eral.