Research On Synchronization And Optimization Of Coupled Complex Systems

Both in natural systems and human social systems,synchronization is very common and plays an important role in the realization of various system functions.With the rapid development of complex networks,synchronization in complex systems becomes more and more significant.With the deepening of research,the problem of how to achieve optimal synchronization has become prominent,because optimal synchronization can not only help people use synchronization behavior to control the complex system,but,in turn,also understand synchronization itself.In this thesis,we mainly focus on the topic of optimal synchronization.In the first chapter,some basic concepts and research backgrounds related to synchronization of complex systems are briefly introduced,including complex networks,basic analysis methods of synchronization,and some traditional optimal synchronization schemes.There are some typical types of complex networks,such as random network,small world network,and scale-free network.In the basic analysis methods of synchronization,the master stability function method is used to analyze the complete synchronization in coupled chaotic system,and the Ott-Antonsen ansatz is used to analyze the synchronization transition of coupled phase oscillator system.Traditional optimal synchronization schemes contain adjusting connection as well as weight between nodes and changing the coupling function.In chapter 2,the approach of achieving network optimal synchronization by introducing a small amount of coupling strength into a single node is studied,and the method based on the eigenvector centrality is proposed.The effectiveness of this method in different network models is verified by numerical simulation.Compared with the traditional centrality,the new method has advantages in improving network synchronization performance.In chapter 3,we pay attention to the effect of self-link on synchronization.Such self-links(autapses)also exist in neural networks.Autapse-centrality is proposed,which can accurately and effectively search the target node and add autapse to the target node,so as to enhance the synchronization of the system.In chapter 4,we study how to set specific phase lag in the coupled phase oscillator system to enhance network synchronization,and verify its performance in promoting and enhancing network synchronization.A reasonable explanation is given from a physical point of view,and the analytic solution of the order parameter is obtained by using the Ott-Antonsen ansatz.In chapter 5,the effect of time delay on the synchronizability of coupled chaotic oscillator is studied by using the two-channel delay coupling scheme.When a second coupling channel is introduced,the synchronization region of the system can be significantly changed.In particular,by making small changes to the time delay,it is found that the synchronization region can be greatly adjusted,or even changed from non-existence to existence.In chapter 6,from the perspective of synchronization,a new module,which can be used in machine learning to improve prediction ability,is proposed.It greatly improves the prediction time of reservoir computing.This module shows a good performance in the prediction of evolution of dynamic variables in chaotic systems.In theory,as long as enough real data can be provided,the long-term prediction of the system can be achieved.