Design And Application Of A New Fractional-order Multi-wing Chaotic System Based On FPGA

Since the value of the next state of the fractional-order chaotic system is not only related to the current state but also related to all previous states,its dynamic characteristics are more complicated than the integer-order chaotic system,and it has a greater application prospect in the fields of secure communication and image encryption.In order to study fractional-order chaotic systems,a new integer-order chaotic system is proposed firstly;then,for fractional-order chaotic systems,there are many solving algorithms,but there is no comparative study,the G-L(Grunwald-Letnikov,G-L)definition method and Adomian decomposition method are comparatively studied;finally,the chaotic pseudo-random sequence generator with large delay is improved.The main research contents and innovations of this thesis are as follows:1.A new integer-order chaotic system with four-wing attractors is proposed,and its dynamics analysis and Implementation on FPGA are carried out.Firstly,the dynamic characteristics of the system are studied from the attractor phase diagram,Lyapunov exponential spectrum and bifurcation diagram.It is found that the system exhibits hyperchaotic characteristics when the parameter c of the system varies in a very large range,and has the characteristics of constant Lyapunov exponent,which has a very rich dynamic behavior.Then the system is discretized by Euler's formula.Based on the fixed-point number,the system is implemented by FPGA,and the hardware achievability of chaotic system with large parameter range is verified.2.The corresponding fractional order chaotic system is constructed based on the integer order chaotic system.The fractional calculus theory is introduced into the integer order chaotic system to obtain the corresponding fractional order chaotic system.3.There are few comparative studies on the two time domain approximation algorithms G-L and Adomian decomposition methods for fractional-order chaotic systems.The dynamic analysis of fractional-order chaotic systems is carried out by using these two time-domain approximation algorithms.And FPGA hardware implementation,so a more comprehensive comparison of the advantages and disadvantages of these two algorithms.Through comparison,it is found that the fractional chaotic system based on Adomian decomposition method not only has richer dynamic characteristics and wider parameter range,but also consumes only half of the hardware resources of G-L definition method for its implementation on FPGA.Therefore,the fractional chaotic system based on Adomian decomposition method has better performance.4.Based on the fractional four-wing chaotic system,a chaotic pseudo-random sequence generator is implemented by FPGA.Taking the fractional-order chaotic system based on Adomian decomposition method as an example,the implementation of each module of the chaotic pseudo-random sequence generator FPGA structure diagram is explained in detail,including chaotic system module,data acquisition module,data buffer module and Ethernet data transmission module.In order to compare the pseudo-randomness of the sequence generated by fractional and integer order chaotic systems,a pseudo-random sequence generator based on integer-order chaotic system is implemented in the same way.5.Aiming at the problem that the chaotic pseudo-random sequence generator requires several clock cycles to output valid data,it is proposed to introduce the S-box and Logistic mapping into the system to improve the system.The improved experimental results show that the sequence generation rate is the same as the system frequency,and thus the sequence generation rates of the fractional and integer order chaotic pseudo-random sequence generators are thirty and ten times higher,respectively.Then the pseudo-random sequence tests are performed on the sequences generated by the four(fractional and integer order and corresponding two improved)chaotic pseudo-random sequence generators,and it is found that all of them can pass the test,and the performance of the fractional order is better than the integer order.The improved performance is reduced,but within acceptable limits.6.Improved integer order and fractional pseudo-random sequence generators are applied to image encryption.It is better to display an improved fractional-order pseudo-random sequence generator to encrypt images from the aspects of encryption effect,histogram and correlation coefficient of adjacent pixels.It is verified that the fractional-order chaotic system is more dynamic than the integer-order chaotic system,and it is more excellent in practical engineering.