The Analysis And Synchronization Issue Of Lorenz System

In 1963,E.Lorenz published the paper "Deterministic Nonperiodic".Flow on Journal of the Atmospheric Sciences,pointing that there existed the necessary connection between weather being unable to react exactly and long-range weather being unable to predictable,i.e.,connection between nonperiodicity and unpredictability. Meanwhile,it pointed that in Lorenz system,a deterministic system,there existed not only regular behavior,but irregular behavior.As the first chaos model,Lorenz system reveals the real meaning of chaos dynamics and bears the predominant status,which is a milestone of chaos development history.Deep research into Lorenz system will be no doubt to significantly promote chaos development.In this paper,first,it summarizes the chaos theories and its development.Then,it discusses the definition of chaos,characters and theories related to Lorenz system.Third, it analyzes an important characteristic value of Lorenz system-Lyapunov exponents and its computing methods,which lays the foundation for the calculation of Lyapunov exponents and analysis of conditional Lyapunov exponents in system synchronization. In the system analysis part of this dissertation,firstly,it introduces the basic property. Then,it lays emphasis on change process of Lorenz system from stability to chaos when the parameters change.Meanwhile,it calculated the concrete parameters when the system enters the chaos state according to the change process.It also solves the values of Lyapunov exponents of each state and validates that the maximum Lyapunov exponents being more than zero is the important sign of system entering chaos state.In the system synchronization research,it utilizes MATLAB to simulate several synchronization methods of Lorenz system.From the synchronization error simulating figures,they clearly show synchronization effects of each synchronization method.At last,it validates a method of utilizing chaos feedback synchronization to estimate the maximum Lyapunov exponents and analyzes the influence of iterative times on the accuracy of the method.This thesis researches into Lorenz system and its synchronization,which has guide effect to other chaos models and theories research.