Research And Applications On Integer-Order And Fractional-Order Multi-scroll Chaotic Systems

The chaos theory has aroused wide attention by scholars when Lorenz found the chaos in the numerical test since1960s. With the deepening research, it is widely used and achieved great development in mathematics, physics, engineering control, chemistry and other fields. Where, the multi-scroll chaotic system is the most important part in the research of chaos theory and application.The thesis has conducted the thorough research to the integer and fractional order multi scroll chaotic system and its application as well. In the aspect of theory, the thesis has made a research on the modeling, control and chaotic dynamic problems of the integer and fractional order multi scroll chaotic system; as to the respect of application, chaotic sequence generated by the multi scroll attractor has been got NIST random tests, and it has been applicated onto the digital image encryption and decryption. At the same time, the thesis has also conducted a research on the high order chua’s circuits and has presented the FPGA hardware realization. The main assistances are as follows:1. Based on the Chua system, the design of controller will breed multi-scroll chaotic attractor. However, because of the Chua system has an odd symmetry; these approaches cannot be applied in even symmetrychaotic system. Therefore, it is vital to find out a method for generating multi-scroll chaotic attractor of even symmetry chaotic system. Based on the generalized Generalized Lorenz system family, this paper raises a double-wing chaotic system with even symmetry.Based on this system, it puts forward a new control method of step-wave function, where generating multi-scroll chaotic attractor within the even symmetry double-wing chaotic system, and exploring the dynamic characteristics of the generating multi-scroll chaotic attractor and presenting numerical simulation and circuit implementation results.2. There are many natural phenomena display the characteristics of fractional order differential equation. The researchers gradually recognize the importance of investigation on fractional order chaotic system. However, research on multi-scroll attractor based on fractional order chaotic system still in the immature stage. This paper constructs the Fractional Piecewise Chen system and Fractional two type function Lii system. Designing a fractional multi-wing chaotic system controller, generating a multi-scroll chaotic attractor and analyzing the dynamic characteristics of multi-scroll chaotic attractor within these two chaotic systems.3. Based on the multi-scroll chaotic system studies, it is going to put forward the application of chaotic sequence generated by multi-scroll attractor into the digital image encryption and decryption. Firstly, present the NIST test, and its working principle. After that, by using multi-scroll chaotic system to generate chaotic sequences, and take the chaotic sequence for a random test of NIST. The test results show that the chaotic sequence Meet the NIST test results, which can be applied to the digital image encryption and decryption successfully. Finally, doing a digital image encryption and decryption experiment in chaos sequence of multi-scroll chaotic system based on FPGA embedded system, and the experimental results are given4. It is going to propose a scheme for constructingthe high order Chua’s circuit, and gives Chua’s circuit equation with five, six and seven orders. Furthermore, take a simulation experiment on high order Chua’s circuit, figure out chaotic attractor of high order Chua’s circuit and examine the chaotic dynamics of high order Chua’s circuit, including the basic dynamic analysis of high order Chua’s circuit chaotic attractor, the balance point, the dynamic characteristics, the bifurcation diagram analysis and Lyapunov exponent. Which obtain the discretization method of high order Chua’s circuit, and successfully implement the high order Chua’s circuit in FPGA.