Stochastic Distribution Synchronization And Control For Complex Dynamical Networks And Its A Pplication

In recent ten years,there has been an increasing number of studies on the synchronization and control for complex dynamical networks by many scholars in different disciplines.This is because it has a wide range of applications in many fields of science and engineering,including communication networks,mobile ad-hoc networks,computer networks,neuronal networks,and social networks.On the other hand,stochastic phenomena generally exist in the real world of nature and human society,and the influence of stochastic factors must be taken into account for the modeling,analysis and control in complex dynamical networks.Therefore,the synchronization and control of stochastic complex dynamic networks has recently become a very important and challenging frontier topic.Unlike previous studies,this paper focuses on stochastie distribute synchronization and control for complex dynamical networks.The main contents of this dissertation are summarized as follows:Firstly,we investigate the practical stochastic synchronisation of coupled har-monic oscillator's and its applications to electrical systems.This study focuses on the practical stochastic synchronization of coupled harmonic oscillators subject-ed to heterogencous noises,where the dissipative and restorative couplings are no longer required in the connected topologies.By employing the variational ap-proach in combination with Lyapunov-like analysis on stochastic dynamic system,some simple yet generie practical stochastic synchronization criteria with directed network topology are established.Different from most previous studies on complete square synchronization for the stochastic networks,three main issues on stochastic synchronization are emphasized,including practical distribution synchronization,stochastic distribution synchronization,and practical mean square synchronization.In addition,because the connectivity of either the dissipative or restorative cou-pling network is no longer required,the network structure can be suitably used to design the control strategy for implementing the desired practical stochastic syn-chronization in practice,which will further be applied to a representative model of circuit system to o show the effectiveness of the developed control methodology.Secondly,we study the stochastic distribution synchronization and pinning con-trol for complex heterogeneous dynamical,letworks.Based on the ergodic theory on stochastic dynamic systems,the invariant measure method is developed to study the stochastic synchronization of complex dynamic network,and some generic s-tochastic synchronization criteria are established for both cases of undirected and directed topology.On this basis.the convergence condition of the stochastic syn-chronization presented in this paper is weak,which are no longer restricted by the rigorous Lipschitz condition.The results are applied to the famous Duffing oscil-lator networks and FitzHugh-Xagumo neuron coupled oscillator systems.The numerical simulation shows the evolution of this stochastic distribution synchro-nization phenomenon and the characteristics of two complex dynamic networks.Finally,we discuss the stochastic distribution synchronizaztion for complex heterogeneous dynamical networks with Markovian switching.On the basis of the previous research,stochastic synchronization of complex networks with Markovian switchig in the sense of convergence in distribution is studied,and the stochastic synchronization criteria for complex networks with the directed topologies are also obtained.It is found that,when the node of complex dynamic network is a general stochastic system,the synchronization performance of complex dynamic network under the probability distribution is effectively improved by using the appropriate Markovian switching control.To this end.the result is applied to a typical switching circuit system,which come out the characteristics of stochastic distribution synchronization for such switched complex networks.