Synchronization Of Coupled Duffing-type Oscillator Dynamical Networks

The synchronization is an important issue of mathematics,physics,biologies and other disciplines in the study of nonlinear problem.At present,it has been widely ap-plied to image processing,laser technology,communication engineering and other fields As a significant feature of coupling oscillators,synchronization between oscillators has always been valued.According to the practical problems and applications,scholars have applied various methods to obtain multiple synchronization results,including Lyapunov functions,stability theorems,matrix measure theory,graph theory and Lin-ear matrix inequality method.Based on the previous researches on synchronization,we are concerned with two kinds of synchronization problems of coupled Duffing-type oscillator dynamical networks by using novel methods,such as integral factor method,constant variable method,and integral inequality techniques.This paper is divided into three chapters,the main contents are as followsIn chapter 1,we review the synchronization theory and its development history,and introduce the research object of this thesis,namely the Duffing-type oscillator dynamic networks.We also discuss the research progress of synchronization problem and briefly reveal the main research contents of this thesisIn chapter 2,the global asymptotic synchronization of coupled Duffing-type os-cillator dynamic network is investigated.Firstly,we establish the drive and response dynamic network model of coupled Duffing-type oscillator.Then,the reasonable con-troller is designed.We get the sufficient conditions for global asymptotic synchroniza-tion of the drive system and response system through using constant variable method,integral factor method,and integral inequality techniques.That is,the drive system and response system achieve synchronization in infinite time.Finally,based on the theoretical analysis results above,we give some examples of numerical simulations,which verify the correctness and effectiveness of the theoretical analysisIn chapter 3,we study the finite time synchronization of coupled Duffing-type oscillator dynamic network.Same as the previous chapter,synchronization problem of drive system and response system is transformed into stability problem of error system Combining the integral inequality,we establish the sufficient conditions for finite-time synchronization of the drive system and response system.To verify the effectiveness of the theoretical analysis,we give some examples of numerical simulations finite time synchronization.Finally,the main research contents of this paper are summarized and the future research directions of coupled Duffing-type oscillator dynamic networks are determined.