Research On Synchronization Of A Class Of Different Order Chaotic Systems

Chaotic synchronization,as a special kind of chaotic control,has the characteristic of nonlinear dynamic system and it is widely used in various disciplines.In this paper,based on the stability theory of integer-order and fractional-order,the model with chaotic phenomenon of different orders is designed reasonably,and the correctness and effectiveness of the controller are verified through a series of methods.The first chapter: Introducing the background and significance of the research,as well as the research status of chaos synchronization at home and abroad.The second chapter: The two definitions and five characteristics of chaos are briefly described,and introducing the integer-order stability theory,including the stability of zero solutions of autonomous systems and zero solutions of non-autonomous systems.The fractional-order stability theory,three main definitions and properties of fractional order calculus are also introduced.In this paper,numerical simulation is carried out for the simple integral-order Qi system and fractional-order Chen system,and the dynamic phenomenon is demonstrated by observing the phase diagram.The third chapter: The integer-order and fractional-order synchronization of a kind of financial chaotic system is studied.According to the knowledge of nonlinear dynamics,adaptive synchronization method,tracking control idea and adaptive rate of unknown parameters are used.The compensator and adaptive controller are defined,and the adaptive tracking controller is designed.The time history diagram of the state variable is shown through MATLAB numerical simulation,and the effectiveness and correctness of the designed controller are proved.Chapter four: From the perspective of scaling factor,different non-singular matrices are selected.Generalized(dislocation)projection synchronization method is used to study the synchronization problem of fractional financial chaos system of different orders.The corresponding controller is designed reasonably,and its validity and correctness are proved by numerical calculation and MATLAB simulation.Chapter five: Summary of the text work and the prospects for chaos synchronization in the future.