Study On Exponential Synchronization Of Two Types Of Complex Networks

Complex networks refer to large-scale networks with complex topology and dynamic properties.The study of complex network is a comprehensive research subject in the fields of mathematics,statistical physics and computer science,etc.The intersection and integration of disciplines make the research of complex network more extensive and more scientifically significant.Exploring and analyzing the synchronization control method of complex network is an important direction of complex network research.Relevant research results have been widely used in electronic circuits,robot formation,information transmission and many other fields,and become the focus of theoretical and applied research.In this paper,based on graph theory,Lyapunov method and hierarchical method,intermittent event-triggered control strategy,intermittent self-triggered control strategy and intermittent noise diffusion layer are presented to study the exponential synchronization of complex networks.The specific research contents are as follows:Firstly,the exponential synchronization in mean square of strongly connected complex networks and non-strongly connected complex networks is studied by using intermittent eventtriggered control strategy and intermittent self-triggered control strategy.We use a more flexible average control rate.A positive lower bound on the trigger interval is given to ensure that Zeno behavior does not occur.Some criteria about complex networks reach exponential synchronization in mean square are obtained.The theoretical results are applied to study the exponential synchronization in mean square of microgrid system,and numerical simulations are given to verify the effectiveness of the control strategy proposed in this paper.Second,a novel intermittent noise-diffusion layer is proposed to synchronize a network system.Different from most of the traditional noise-induced synchronization or noise stabilization(noise exists in nodes of the network),we give an intermittent noise-diffusion layer(the noise exists in the edges of the network)to study the almost sure exponential synchronization.The theoretical results show that the general network system can be synchronized in the almost sure sense as long as the topological structure of the network in the intermittent noise-diffusion layer is an undirected connected graph.Two examples are proposed to illustrate the theory obtained.