Synchronization And Structure Identification Of General Stochastic Complex Networks Via Finite-time

In recent years, more and more scientific workers devoted themselves tothe dynamics of complex network, especially synchronization and control problem ofcomplex network. With further research, it was found that stochastic disturbances isinevitable in the propagation process of network. Reducing the impacts of stochasticdisturbances on the system and maintaining system stability is very important.Meanwhile, in the study of the synchronization and control of complex network, mostexisting studies are based on infinite-time for analysis. Whereas, compared with thesynchronization within infinite-time, finite-time synchronization is more in line withthe needs of our real life. The issue of how to obtain finite-time synchronization ofcomplex network and topology identification is a challenge for us.The following two points have been studied in this paper:(1)Finite-time synchronization of the unified chaotic system with stochasticdisturbances is investigated, in which the perturbation is a Wiener process ofone-dimensional standards. Based on finite-time stochastic Lyapunov stability theoryand It formula, three steps are presented to consecutively design three controllers toguarantee the finite-time mean-square asymptotical synchronization of thedrive-response systems.(2)Based on adaptive synchronization, structure identification of general complexnetwork with stochastic disturbances, which is a zero-mean real m-dimension Wienerprocess, is investigated. The External coupling matrix of the network needs not to bediffusive, symmetric or irreducible and is applicable to both directed and undirectednetworks. Based on finite-time stochastic Lyapunov stability theory, adaptive controland It formula, some novel criteria for the finite-time stochastic synchronizationbetween drive and response complex networks were derived. Simultaneously, thestructure of the drive complex network is identified.Finally, numerical simulations are provided to illustrate the correctness andeffectiveness of the theoretical results.