A New Method Of Generating Multi-scroll Attractors And Circuit Design Based On Memristor

Comparing with traditional chaotic systems, multi-scroll chaotic systems have more complex dynamic characteristics and more secret key parameters. Therefore, it is more suitable for chaotic secure communication. In the past two decades,researchers at home and abroad have a lot of research on the method of generating multi-scroll chaotic attractors. But the construction methods obtained are about the same, that are constructed by different functions so as to generate multi-scroll chaotic attractors. The main problem of this methods is complex mathematical operations and difficulties in realizing circuit. Therefore a simple method of achieving multi-scroll is explored, which will bring convenience for the complex chaos into practical application.The fourth basic electronic components―memristor applied to chaotic circuit design is a new direction in the development of chaotic circuit. Comparing with traditional chaotic circuit, memristive chaotic circuits have more complex chaotic characteristic. 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. Focusing on the key problems in actual application, in this dissertation, we focus mainly on the generation method of multi-scroll chaotic attractors and the designing of memristive chaotic circuit. The concrete research contents and results summarized as follows:(1) A new means of multi-scroll chaos based on pulse control is proposed. The new method can achieve the translation or extension of the system equilibrium point,and then generate multi-scroll chaotic attractors as long as a suitable pulse source is joined in a particular location of the double scroll chaotic system. Then the method is successfully applied in Chua’s circuit, Jerk system and analogous Lorenz system,generating a series of different multi-scroll and multi-blade butterfly chaotic attractors.Compared to traditional methods, the proposed method is without constructing system nonlinear control function and designing complicated realized circuit. Therefore this method greatly simplifies the design of multi-scroll chaotic circuit no matter in the mathematical analysis or the circuit implementation.(2) A systemic method of generating compound chaotic attractor is presented.First of all, a single parameter unified chaotic system is constructed, which can bedecomposed into two subsystems when the parameter takes different values, getting two kings of chaotic attractors. Then the pulse signal is used to to realize the different value of system parameters, thus it can realize the recombination of the two chaotic circuits of subsystem. The paper successfully realized two composite of three kinds of attractor under the Lorenz system, verifying the correctness of the proposed method.A several different types of chaotic circuit are designed and a series of different chaotic attractors are presented.(3) A five order chaotic circuit with HP memristors is designed, which is consisted of a flux-controlled memristor and a charge-controlled memristor. The dynamic properties of the circuit are demonstrated by means of general dynamics analysis. In order to ensure the occurrence of chaos behaviors in the circuit, simulators of the charge-controlled memristor and the flux-controlled memristor are designed with convention electronic devices, and Pspice simulation is conducted on the resulting circuit. Pspice simulation results verify the correctness of the theorectical analysis.(4) A new kind of chaotic circuit is designed by using LC oscillator and magnetic control memristor. By changing the control parameter, the circuit evolves into different orbits, such as periodic orbits 、 double-scroll and single-scroll. In order to control the proposed chaotic circuit, analog time-delay feedback control method is investigated. The numerical simulation results show that the method can achieve chaos stabilization control.Circuit experiment are conducted in the end, verifying the correctness and the effectiveness of the chaos stabilization control.(5) A series of new chaotic circuit Memristor are gotten by selecting current feedback operational amplifier as active device and meanwhile combining the four basic components(Resistor, Capacitor, Inductor, Memristor) by utilizing the port characteristics of the device skillfully. The simulation results show that the circuits can produce a kind of strange attractor that is different from chua’s circuit, which enrich the content of chaotic attractor memristor.