Research On Synchronization Control Of Complex Network With Multi-delay And Multi-weight

In the past two decades,complex dynamic networks have been the focus of attention.Many science and technology systems can be modeled as complex dynamic networks.Time delay is common in many real networks,such as biological networks,communication networks,physical networks and so on.The occurrence of time delay often affects the performance of the system,resulting in vibration and even instability of complex traffic networks.Therefore,in recent years,complex network systems with time delay have attracted wide attention.However,the delay of most literature studies is single,and the real complex networks in life usually contain multiple delays.Based on the above reasons,many scholars have introduced the idea of network splitting into their research,and established a multi-delay complex network model.However,the weights of different nodes in each subnetwork are not reflected.At present,many researches on complex networks have made some attempts at decentralization.In the research of complex network synchronization control,some researchers use the idea of network splitting and introduce the concept of weight to propose a complex network model based on weight.This thesis makes a further research based on the relevant research results of the existing complex dynamic network system model.At present,using the idea of network splitting to analyze and study the multi-edge complex network model has attracted the attention of many scholars.Moreover,compared with the research of small-world network,scale-free network and other network models,the related research of multi-edge complex network model based on split idea is not mature enough,and there are still many gaps to be filled,so it has a better research space.This thesis summarizes the related research of the existing time-delay complex network model and weighted complex network model.The delay complex network system mainly reflects the characteristic of the transmission speed difference of the system.Compared with the simple merging of the early system models,this model can better reflect the delay characteristics of the real system.It can better describe some complex network systems which can not be merged due to the large speed difference between edges.The corresponding weight complex dynamic network system model focuses on the different weights of different nodes and edges to the system itself.Through the observation of the above two models,it can be found that although the twomodels are different in describing the system characteristics and topology,and each has its own advantages,they are essentially based on the idea of network splitting to improve the previous dynamic complex network model.and the dynamic complex network generally has the characteristics of many nodes and complex structure,so the split sub-network still has the properties of complex network.Based on the above theories and conjectures,an in-depth study has been carried out,and the main works are as follows:The main contributions of this thesis are as follows:(1)Through the in-depth research and understanding of the complex network model of time-delay multiple edges and weighted multiple edges,the idea of network splitting is used to establish a relatively more general.A multi-delay and multi-weight complex network model which can reflect various characteristics of the system(delay,weight,etc.)at the same time.(2)The synchronization ability of multi-delay and multi-weight complex network model is studied,and the synchronization criterion of multi-delay and multi-weight complex network system under uncontrolled condition is obtained.at the same time,the linear feedback controller and adaptive controller are designed for the new model established in this thesis,and the corresponding synchronization decision theorem is obtained by proof and verified by numerical simulation.(3)According to the actual needs,the idea of pinning control is introduced to establish a multi-time-delay and multi-weight complex network containment control model.Furthermore,the corresponding linear feedback pinning controller and adaptive pinning controller are designed,the synchronization conditions are given through proof,and the numerical simulation results of the synchronization effect are given.