Research On Control Of Fractional-order Chaotic Systems

In the field of nonlinear science,the study of chaos is getting deeper and deeper.The focus of chaos research is how to make better use of chaos system,the concept of chaos control has been put forward,its purpose is to effectively remove the "harmful" components in chaos,a lot of valuable research results have been achieved on chaos control.With the introduction of fractional calculus,the study of fractional chaotic systems has become a hot topic.Compared with integer order chaotic systems,it has more complex dynamic characteristics,so it has a wide application prospect in the field of system security and signal processing.This paper analyzes the dynamic characteristics of fractional-order An system and fractional-order Coullet system in chaotic motion.By numerical calculation,the order range and parameter value range of the two systems in chaotic state are obtained.It is found that fractional-order chaotic systems have different motion states.When fractional-order An system and fractional-order Coullet system are in chaotic state,their chaotic attractors have complex topological structure.The chaos control of fractional-order An system and fractional-order Coullet system is studied by linear feedback control method,parametric periodic perturbation method and periodic excitation method.The chaos control of two fractional-order systems is realized by adjusting the parameters of the controllers added by different methods,and the parameter value range of effective control is given.Numerical results show that these three methods can control the chaos of fractional order system.Finally,design the circuits of integer and fractional order An system and Coullet system.The attractors of integer and fractional order systems with different parameters are obtained by Multisim simulation,which is consistent with the numerical results,and the linear feedback control of fractional Coullet system is simulated and controlled.