Research On Synchronization Problem Of Markov Switching Stochastic Network

With the rapid development of network science,human life has entered the era of complex network,human production and life has been inseparable from complex networks,such as the Internet and mobile communication networks,social networks,power networks,neural networks,traffic network and metabolic networks.Therefore,the complex network attracts the extensive attention of experts and scholars from various fields,and quickly becomes one of the hot topics in scientific research.Synchronization of complex networks refers to the process of nodes in the network,under the interaction between nodes,starting from the initial state,the dynamic behavior between each node gradually tends to the same state with the evolution of time.For example,fireflies will glow at the same time,and the fish will maintain the same pattern and swim together.However,most of the networks in real life can not synchronize themselves,so many effective control methods are proposed and applied to network synchronization,according to the control time can be divided into continuous control and discontinuous control,while non-continuous state control includes pulse control,periodic intermittent control,aperiodic intermittent control and so on.The discontinuous control strategy greatly reduces the control cost by reducing the control time,which is favored by the majority of network synchronization researchers,especially the aperiodic intermittent control strategy has been widely concerned.What can not be ignored is that the actual network in nature due to the delay of information transmission between nodes and so on,almost all the actual network has time lag phenomenon,such as long transmission lines,pneumatic systems,nuclear reactors,rolling mills,hydraulic systems and manufacturing processes.Time delay is obviously a factor that can not be ignored in the synchronous analysis of complex networks,so the stability analysis and synchronous control of time-delay complex network systems have attracted wide attention of many scholars.Time delay will have a great impact on the system,will reduce the performance of the system or damage the stability of the system,so it is worth studying how to synchronize the system when the delay exists at that time.At the same time,environmental uncertainty such as noise,violent external attack and mechanical instantaneous failure also make the actual network show obvious stochastic characteristics.So in recent years,a lot of research results have emerged on the stability and synchronization of stochastic networks with mixed time delay,but most of the random perturbation items in the existing results are one-dimensional,that is to say,all nodes are disturbed in the same way,and obviously such considerations are not comprehensive.The Markov switching network driven by continuous time Markov chain has been favored by researchers in recent years,and many achievements have emerged in the study of the stability and synchronization of Markov switching stochastic networks.Therefore,this dissertation is devoted to the study of the synchronization problem of Markov switching stochastic networks with mixed time delay,and the stochastic perturbation items in this model are multidimensional and more general.The research work is mainly divided into the following two parts:First,the synchronization problem of stochastic networks with Markov switching under aperiodic intermittent pinning control.The aperiodic control is to divide the arbitrary time interval into the control interval and the rest interval where the interval length is not fixed,and control some nodes in the network in the control interval,which is a control method that combines the control of the pin and the control of the interval.Strategy.This strategy greatly promotes the reduction of control costs while saving control time,and has been favored by many scholars.So we use aperiodic intermittent pinning control to study the synchronization problem of Markov switched stochastic networks.In the proof process,we use the Lyapunov function and the Gronwall inequality to make the proof process simple,correct and efficient.In the process of proof,we use Lyapunov function and Gronwall inequality to make the proof process concise,correct and efficient.The second is to study the synchronization problem of Markov switching stochastic networks with mixed time delay by using aperiodic quantization pinning control,and by constructing a reasonable time-dependent Lyapunov function,With the help of convex combination and other mathematical theoretical knowledge,some sufficient conditions to ensure the synchronization of Markov switching stochastic networks with mixed time delay are obtained through strict mathematical proof.It is worth noting that this is the first time that the quantization controller has been applied to the synchronous study of the Markov switching stochastic network,and through numerical simulation,we find that the aperiodic quantization control has achieved more ideal results in synchronous effect,control time and control cost.