Research On Synchronization Control Of Several Classes Of Chaotic Systems

Nonlinear science has developed rapidly since the middle of the 20th century.Chaos is a special form of motion in nonlinear dynamical systems.Chaos theory has attracted widespread attention since its discovery.Due to the special characteristics of the chaotic systems,their trajectories are unpredictable.Chaos synchronization can make the trajectories of two or more chaotic systems consistent.At present,chaos synchronization theory has been combined with many subjects,such as information science,biology,physics and so on.Therefore,further research and enrichment of chaos synchronization theory has important significance of theoretical analysis and the value of practical application.This thesis studies the synchronization of several classes of chaotic systems,and considers the following problems:(1)Hybrid Synchronization and Application of Multiple Chaotic SystemsAt present,chaos synchronization models mainly focus on single-driving and single-response models.This thesis deeply explores the synchronization model of multiple chaotic systems based on previous work,that is,the synchronization models of multiple driving and single-response systems.First of all,this thesis designs a synchronization method for the hybrid synchronization of multiple chaotic systems based on the synchronization model of multi-driving and single-response systems,where the parameters of the driving systems are unknown.And the general synchronization controllers and identification rules of unknown parameters are designed by using Lyapunov stability theory and adaptive control methods.Afterwards,numerical simulation was carried out using Matlab software to verify the theoretical analysis.Finally,this thesis uses the designed synchronization method of hybrid synchronization of multiple chaotic systems and classic plaintext association scrambling encryption algorithm to realize the encryption and decryption of digital images,and verifies the availability of the synchronization method.(2)Control and Synchronization of Passively Controlled Complex Chaotic SystemsThere is a lot of work on the research of the control and synchronization of chaotic systems by passive control theory.However,there is very few work on the combination of complex chaotic systems and passive control theory.Therefore,this thesis takes the complex Lorenz system as an example.First,a feedback controller is designed to control the complex Lorenz system to the expected period based on passive control theory.Then,the identification rules of synchronous controller and unknown parameters are designed based on passive control theory and adaptive control method,and the complex Lorenz system with unknown parameters is successfully synchronized under different initial conditions.The study of this problem has further enriched the chaos synchronization theory and provided a theoretical basis for further research.