Research Of The Multi-wing And Multi-scroll Chaotic System

Chaos theory is an important branch of nonlinear science, it is a frontier which developed in recent decades, it is one of the three important scientific discoveries of the twentieth century like quantum physics and relativity, so chaos theory has a broad research prospect and important significance. In Twenty-first Century, the application of chaotic systems is one of the key research directions of nonlinear science research, it can be explored from two directions: one is exploring the new method to generate the multi-scroll(multi-wing) chaotic attractors, this method can produce a multi-scroll(multi-wing) chaotic signal which has a higher degree of complexity; the other is the design and implementation of chaotic circuit. Along with the chaos theory is more and more widely applied in the practical engineering, making better use of the memristor and designing all kinds of new-type memristive chaos circuit, has important practical significance. This thesis work focuses on the multi-scroll(multi-wing) chaotic systems and the designing of memristive chaotic circuit. The concrete research contents and results summarized as follows:(1) Derived a unified chaotic system under the generalized Lorenz system. Then it can be achieved the classic butterfly attractors and piecewise linear chaotic systems for the generalized Lorenz chaotic system which are two kinds of chaotic system through settings of the different system parameters, including the classical Lorenz system, the classical Chen system, the classical Lü system, the composite structure of Lü attractor,the composite structure of Chen attractor, the piecewise linear Lorenz system, the piecewise linear Chen system and the first kind of simulation Lorenz system. In order to generate the chaotic attractors of the subsystems in circuit, the realizing circuit of unified system is designed. And the unified chaotic system can be realized by changing the state of the switches in the control circuit. Finally, the unified system circuit is simulated by Pspice, the simulation results are in good agreement with the numerical simulation, which verifies the correctness of the designed system and the physical realization.(2) Aiming at four-dimensional chaotic systems which can generate four-winged chaotic attractors, a new multi-wing unified chaotic system was built by introducing a plurality of linear and nonlinear state feedback controls. It can be achieved the real four-winged chaotic attractors which is symmetric about the origin, the butterfly shapedchaotic attractor, bat-shaped chaotic attractors and the new type of the multi-wing chaotic attractors by changes of the system parameters. A detailed discussion of system parameters on the sensitivity of chaotic behavior was made by the numerical simulation and theoretical analysis to the basic dynamic characteristics of the system, such as phase diagrams, dissipative analysis, power spectrum, Poincare section, Lyapunov exponent spectrum and bifurcation diagrams.(3) A novel parallel memristor chaotic circuit was constructed by a flux-controlled memristor, an inductance, a capacitance. The dynamic properties of the circuit are demonstrated by means of dynamical methods. In order to confirm the proposed occurrence of chaotic behavior in the circuit, an analog Pspice implementation of this circuit was presented. The simulation results are well consistent with theoretical analysis and numerical simulation results. Without changing the shunt memristor circuit chaotic structure of the original system, we introduced the excitation pulse, adjusted the amplitude and width of the suitable pulse to achieve expansion of the system equilibrium point, to result in a multi-scroll chaotic attractors, and then put forward a simple and practical memristor multi-scroll chaotic circuit. Simulation results showed that the system can generate a strange attractor different from the Chua's circuit, and the number of the attractors increased as the number of the excitation pulse.