Study On Dynamic Behavior And Synchronization Control Of Fractional Order Chaotic Systems With Time Delay

Time delay exists widely in nature,in the actual system,due to the mechanical,friction and other factors,there is always a time delay phenomenon,such as in the fields of economy,biology,chemistry,machinery,physics and engineering.Because the fractional order chaotic system with time delay is closer to the real life and the dynamic behavior is more complex.Therefore,it is of great theoretical significance and practical value to study fractional order chaotic system with time delay.On the one hand,the research on the dynamic behavior of fractional order chaotic system with time delay is still in its infancy,and many aspects need to be improved.On the other hand,the synchronization control of fractional order chaotic system with time delay is of great value in the field of secure communication.However,there is little research on the synchronization control of fractional order chaotic system with time delay.In view of the above reasons,the main research work of this thesis is as follows:(1)First of all,a kind of algorithm for fractional order delay differential equation is introduced.The dynamic behavior of fractional order Liu chaotic system with time delay,fractional order Chen chaotic system with time delay and fractional order financial chaotic system with time delay are studied,which in the condition of different time delay,thereby,the range of time delay is obtained when the system is in a chaotic state.In addition,fractional order Qi chaotic system with time delay is proposed,and its dynamic behavior is studied.(2)In view of a class of synchronization control problems about uncertain and time delay fractional order chaotic systems with nonlinear uncertain terms and external disturbance,based on Barbalat lemma and adaptive control theory,the adaptive controller is designed.The controller is independent of the system mathematical model.By using the designed controller,the synchronization control of uncertain fractional order Liu chaotic system with time delay,uncertain fractional order Chen chaotic system with time delay and uncertain fractional order financial chaotic system with time delay are realized.The simulation results show the effectiveness of the controller.(3)In view of the synchronization control problem for the different structure fractional order time delay chaotic system with completely unknown nonlinear uncertain terms and external disturbance,based on the Lyapunov stability theory and Barbalat lemma,an adaptive radial basis function(RBF)neural network controller and its integer order adaptive laws of parameters are designed.As for the stability proof,first,a kind of integer order derivative square Lyapunov function is constructed,based on some lemmas,the synchronization error is proved to be zero.Using this method,the fractional derivative of square Lyapunov function is avoided,and the parameters adaptive laws are of integer order.Theoretical proof and numerical simulation show that the control method is correct and effective.Compared with the current synchronization method,the designed controller in this thesis does not depend on the system model,and fast response speed,high control precision,strong anti-interference ability and good robustness,therefore,this control method not only has important theoretical significance,and has broad application prospects in the field of secure communication.(4)At present,fractional order calculus system research mainly focus on setting a fractional order as a constant,but in the many actual physical systems,fractional order often varies with time.In this thesis,the variable order fractional calculus is introduced into the time delay chaotic system,which enriches the current chaotic system.A method for calculating fractional order delay differential equations with variable order is introduced,the dynamic behavior of variable order fractional order Liu chaotic system with time delay,variable order fractional order Chen chaotic system with time delay,variable order fractional order financial chaotic system with time delay and variable order fractional order Qi chaotic system with time delay are studied by using this method.