Chaotic Synchronization Of Discrete Fractional Bragg Acousto-Optic Bistable System

In recent years,the control and synchronization of continuous fractional-order chaotic systems have been widely studied.However,the study on the dynamical behavior of discrete fractional differential systems is less,and the synchronization control of discrete fractional order chaotic systems needs further improvement and development.Based on the Caputo like difference equation,a class of discrete fractional Bragg acousto-optic bistable systems is constructed,and its dynamics behavior is studied.The system is studied by using parameter adaptive method,driving parameter method and feedback control method for its chaotic state.The synchronization criteria are obtained.Numerical simulation results show that the three methods can realize the synchronization of the system.The specific contents are as follows:The first chapter briefly introduces the research background and current situation of this topic,and then expounds the main work and general structure of this paper.In the second chapter,the definition,theorem and properties of fractional difference correlation are introduced.A class of discrete fractional Bragg acousto-optic bistable systems is constructed and its dynamic behavior is studied.From the third chapter to the fifth chapter,the synchronization control of discrete fractional Bragg acousto-optic bistable system is realized by parameter adaptive method,driving parameter method and feedback control method,and the synchronization criterion is given.Through numerical simulation,the feasibility of three kinds of synchronization methods is validated.The sixth chapter summarizes the main work and deficiencies of this thesis,and forecasts the research content and direction of chaotic synchronization control of discrete fractional order system.