Analysis And Hardware Implementation Of A Class Of Fractional Order Four-wing Chaotic Systems

Since 1970s,the research on the characteristics and applications of chaotic systems has been attracting a number of researchers' concern.Because fractional-order chaotic systems have more complex dynamic characteristics,the researches on the characteristics and applications of fractional-order chaotic systems have become a new hot topic.In this paper,based on a class of fractional-order chaotic systems with four-wing chaotic attractors,the dynamic characteristics,hardware implementation,chaos synchronization control and video image encryption are investigated.The main work of the thesis is as follows:1.The dynamic characteristics of the fractional-order chaotic system with four-wing chaotic attractors are studied.Firstly,the equilibrium points of this class of fractional chaotic systems are studied,and the types of equilibrium points of this class of fractional chaotic systems are determined.Secondly,the dynamic characteristics of this kind of fractional chaotic system are analyzed by time-frequency domain transformation method and predictor-correction method.The Lyapunov exponent diagram and bifurcation diagram of this kind of fractional-order chaotic system are given,and the existence of coexisting attractor is explained by phase locus.2.This kind class of fractional-order chaotic system is implemented by analog circuit and digital circuit,respectively.The analog circuit of fractional-order chaotic systems is implemented by addition circuit model,subtraction circuit model,multiplication circuit model and integral circuit model.Also,the digital circuit of fractional-order chaotic system is constructed by DSP Builder,then VHDL language is exported,compiled and downloaded to the FPGA experimental platform.The results of analog circuit and digital circuit are consistent with those of numerical simulation.The feasibility of hardware implementation of this kind of fractional-order chaotic systems is verified.3.The synchronization control methods of fractional-order chaotic systems are studied by means of nonlinear state feedback synchronization,projective synchronization and synchronization with different structures,respectively.The main research contents are as follows:the driving equation and response equation are constructed,the synchronous trajectory and error curve between driving equation and response equation are analyzed and calculated to verify the rationality and validity of the synchronous control method.On this basis,the synchronization control is realized by analog circuit and digital circuit,and the results of synchronization circuit is consistent with those of numerical simulation.The synchronous circuit provides a practice model for the application of this kind of fractional-order chaotic systems.4.The problem of video image encryption for this kind of fractional chaotic systems is studied on FPGA platform.The results show that this kind of fractional chaotic system can be used in video image encryption.Based on histogram and correlation coefficient between adjacent pixels,ciphertext sequences are analyzed,and the advantages of this kind of fractional chaotic system for video image encryption are further illustrated.