Synchronization Analysis For Two Types Of Lévy Noise Controlled Systems

At present,the study of networks is ranging from ecology,physics,social science and many other disciplines.As a typical collectively dynamical behavior,synchronization of networks not only can well explain many actual phenomena but also has many potential applications in neuroscience and computer science,and is a hot research topic in control and engineering.Therefore,it is of great significance to study synchronization of networks.In general,many networks are subject to disturbances in the real environment that can be simulated as noises.For decades,noises have been widely studied,such as white noise,colored noise,Lévy noise,and so on.Therein,Lévy noise driven by Lévy process has attracted wide attentions from scholars in recent years.In addition,time delays are ubiquitous and taken into account as an inevitable factor,which may affect the networks dynamics behavior.From the practical point of view,it is more suitable to consider the influence of noises,time delays and other factors on networks.In the study of networks dynamics behavior,different control strategies are usually adopted to realize synchronization.Moreover,continuous controls need continuous time state observations of vertexes,which is difficult and expensive in practice.Compared with continuous controls,intermittent control has many advantages of reducing the amount of transmitted information and economic applicability.Thus,this paper investigates the synchronization of Lévy noise coupled systems on two kinds of networks via intermittent control.On the one hand,in general,the digraph corresponding to network is strongly connected or without strong connectedness.However,most of the existing results are base on that the digraph corresponding to network is strongly connected or contains a root spanning tree.Nevertheless,many real networks are without strong connectedness.In the second chapter of this paper,the synchronization of Lévy noise coupled systems with time delays on networks without strong connectedness is studied via periodically intermittent control.By the theory of asymptotically autonomous systems,a graph-theoretic approach,a hierarchical approach,Lyapunov method and some techniques of inequalities,a new set of synchronization criteria are obtained,and the designed range of intermittent controller parameters is shown.Theoretical results show that the intensity of control,the coupling strength and the perturbed intensity of noise are the main factors affecting synchronization.In theoretical application,the synchronization of a kind of coupled oscillators with time delays and Lévy noise on networks without strong connectedness is researched.Moreover,a numerical example is provided to demonstrate the disturbance effects of Lévy noise and the coupling factor for synchronization of systems,and the effect of periodically intermittent control,which explains the feasibility of the theoretical results.On the other hand,networks generally have single-weight or multi-weights ones.In actual networks,such as social network and traffic network,there may be multi-weights between network vertexes.Therefore,it is of practical significance to consider networks with multi-weights.In the third chapter of this paper,the synchronization of Lévy noise coupled systems with time delays on a multi-weights network is studied via aperiodically intermittent control.By a graph-theoretic approach,Lyapunov method and some techniques of inequalities,two kinds of synchronization criteria are obtained,and the designed range of intermittent controller parameters is shown.Therein,the intensity of control,the coupling strength and the perturbed intensity of noise are the main factors affecting synchronization.The criteria do not need that each subgraph is strongly connected.In theoretical application,the synchronization of a kind of Chua's circuits with time delays and Lévy noise on a multi-weights network is researched,and numerical simulations are given to demonstrate the effectiveness of the theoretical results.