Analysis And Implementation Of A Chaotic System And Its Fractional Order Model

In recent years,the theory and application of chaos have rapidly developed and attracted extensive attention of researchers.Among them,the characteristic analysis and hardware implementation of chaotic systems are two main research directions.The former can be used to help in-depth analysis of chaotic dynamics and find out the causes of chaos generation,which can avoid or utilize chaotic phenomena,such as avoiding chaotic phenomena in DC/DC converters and motors,or using chaos in detecting signal parameters and encrypt images and so on.The latter can help to use chaotic model in practical application and solve some engineering problems,such as laser technology,high power microwave source and secure communication and so on.In this paper,a new three-dimension chaotic system and its fractional order model are studied in detail.By analyzing the chaotic dynamic behavior and mechanical characteristics,some unique properties of the three-dime nsion chaotic system are found.In addition,this paper also designs the hardware circuit and implement the chaotic system,and presents an application example of secure communication.The main work of this paper is as follows:(1)Aiming at a newly proposed three-dimension chaotic system,the characteristics of the system are further investigated,especially,from the point of view of mechanics and energy.Firstly,the system is transformed into Kolmogorov’s dynamic system,which is decomposed into the corresponding form of torque.Then,through the analysis of each torque,it is found that inertia torque and non-Rayleigh dissipation are the main causes of chaos generation in the system At the same time,Hamiltonian and Casimir energy functions are used to study the influence of energy conversion on the dynamic characteristics of the system.(2)The characteristics of the fractional order model of the chaotic system are further studied,including stability,phase trajectory,Lyapunov exponents,order bifurcation and Poincare map and so on.It is found that the fractional order system has more complex dynamic characteristics than the integer order system.(3)The three-dimension chaotic system and its fractional order model are implemented by designing analog circuit.The results of the circuit experiment are consistent with those of the numerical simulation,which shows that the system can be realized by analog circuit and provides the corresponding physical model for the application of the system.(4)The digital circuit of the three-dimension chaotic system is also implemented by FPGA.At the same time,based on the synchronization method of nonlinear state feedback,the synchronization of the system is implemented,and an application circuit based on chaos masking secure communication is presented.In a word,this paper investigates the characteristics of a three-dimension chaotic system and its fractional order model,finds out the causes of chaos generation and the influence of energy change on the dynamic characteristics of the three-dimension chaotic system,and implements the system and its synchronization,which provides a hardware model for its application in engineering.