多涡卷吸引子产生新方法与忆阻型混沌电路设计
发布时间：2018-09-03 17:10
【摘要】：多涡卷混沌吸引子与传统的双涡卷混沌吸引子相比,具有更多的密钥参数及更复杂的动力学特性,因此其更适合混沌保密通信。近二十年来,国内外研究者对多涡卷混沌吸引子产生方法进行了大量探索。但得到的构造方法大体相同,均是通过构造不同的非线性函数从而达到产生多涡卷混沌吸引子的目的。此类方法存在的主要问题是数学运算复杂,电路实现困难。因此寻找一种简便的多涡卷实现方法,打破传统方法中设计各类复杂非线性函数的限制,将为多涡卷混沌电路走向实际应用产生便利。将第四种基本电子元件忆阻器应用到混沌电路设计中,是近年来混沌电路发展的一个新方向。与传统混沌电路相比,忆阻混沌电路具有更复杂的混沌特性。随着混沌理论在实际工程中应用越来越广泛,如何更好的利用忆阻器的非线性,设计各类新型忆阻型混沌电路,具有重要的实际意义。着眼于混沌实际应用中的重点问题出发,本论文的主要工作集中在多涡卷混沌吸引子产生方法研究和忆阻混沌电路设计两个方面。具体研究内容及成果总结如下:(1)提出了一种基于脉冲控制法的混沌多涡卷实现方法。该法只要在双涡卷混沌系统中特定位置加入合适的脉冲源,即可实现系统平衡点的平移或扩展,从而实现多涡卷混沌吸引子的产生。将该方法成功应用于蔡氏电路,Jerk系统及模拟Lorenz系统中,产生一系列不同的多涡卷和多翼蝴蝶混沌吸引子。相比传统方法,新方法无需构造系统非线性控制函数,及设计复杂实现电路。因此该方法无论在数学分析还是在电路实现上,都简化了多涡卷混沌电路的设计。(2)提出了一种复合混沌吸引子的系统实现方法。首先构造一个统一的混沌系统,即当系统参数取不同的值时,该系统可分解成两个子系统,相应得到两类混沌吸引子。然后用脉冲信号去实现系统参数的不同取值,即可实现子系统混沌吸引子的复合。利用该法成功实现Lorenz系统族下三类吸引子的两两复合,Matlab与电路仿真结果均验证了该方法的有效性。设计三类不同的忆阻混沌电路,得到一系列不同的混沌吸引子。(3)对蔡氏电路进行改造,设计了一个含两种忆阻器的五阶混沌电路。采用常规动力学分析手段研究了系统的动力学特性。利用基本元器件设计了忆阻器模拟器,并对所设计混沌电路进行Pspice仿真。得到的Pspice仿真结果与理论分析一致。(4)采用LC振荡器和磁控忆阻器设计了一种新的混沌电路。动力学分析表明改变电路参数,可产生双涡卷、单涡卷、周期态等不同相轨道。为了实现电路的混沌控制,设计了一种模拟时滞反馈控制电路,Matlab仿真结果表明该控制器可实现了所提混沌电路的稳定控制。最后设计了相应的电路实验,从示波器上观察到了混沌吸引子及混沌控制相图。(5)选择电流反馈运算放大器作为有源器件,同时巧妙利用该器件的端口特性将四种基本元件(电阻,电容,电感,忆阻器)进行有机结合,得到一系列新的忆阻混沌电路。仿真结果显示这些电路产生一类不同于蔡氏电路的奇怪吸引子,丰富了忆阻混沌吸引子的内容。
[Abstract]:The multi-scroll chaotic attractor has more key parameters and more complex dynamic characteristics than the traditional double-scroll chaotic attractor, so it is more suitable for chaotic secure communication. In the past twenty years, many researchers at home and abroad have explored the generation methods of multi-scroll chaotic attractor. The main problem of this kind of method is the complexity of mathematical calculation and the difficulty of circuit realization. Therefore, a simple method of multi-scroll realization is proposed to break the limitation of traditional methods in designing various kinds of complex nonlinear functions, which will lead to multi-scroll chaos. In recent years, the application of memristor, the fourth basic electronic element, to the design of chaotic circuits is a new direction of the development of chaotic circuits. Compared with traditional chaotic circuits, memristor chaotic circuits have more complex chaotic characteristics. With the application of chaotic theory in practical engineering more and more widely, how about It is of great practical significance to make better use of the nonlinearity of memristors to design all kinds of new memristor chaotic circuits. Focusing on the key problems in the practical application of chaos, the main work of this paper focuses on the generation method of multi-scroll chaotic attractors and the design of memristor chaotic circuits. The results are summarized as follows: (1) A chaotic multi-scroll realization method based on pulse control method is proposed. The method can realize the translation or expansion of the equilibrium point of the system and the generation of multi-scroll chaotic attractors by adding a suitable pulse source at a specific position in the dual-scroll chaotic system. A series of different multi-scroll and multi-wing butterfly chaotic attractors are generated in a unified and analog Lorenz system. Compared with the traditional methods, the new method does not need to construct the nonlinear control function of the system and to design complex implementation circuits. A method of system realization of compound chaotic attractor is proposed. Firstly, a unified chaotic system is constructed, that is, when the system parameters are different, the system can be decomposed into two subsystems, and two kinds of chaotic attractors can be obtained accordingly. Three different kinds of memristor chaotic circuits are designed and a series of different chaotic attractors are obtained. (3) The Chua's circuit is reformed and a five-order memristor is designed. Chaotic circuit. The dynamic characteristics of the system are studied by means of conventional dynamic analysis. A memristor simulator is designed with basic components, and the designed chaotic circuit is simulated by Pspice. The results of Pspice simulation are consistent with the theoretical analysis. (4) A new chaotic circuit is designed by using LC oscillator and magnetron memristor. The mechanical analysis shows that different phase trajectories such as double scroll, single scroll and periodic state can be produced by changing the circuit parameters. In order to control the chaos of the circuit, an analog time-delay feedback control circuit is designed. The simulation results of MATLAB show that the controller can realize the stable control of the proposed chaotic circuit. The chaotic attractor and the chaotic control phase diagram are observed in the waveguide. (5) A current feedback operational amplifier is selected as the active device, and four basic elements (resistance, capacitance, inductance, memristor) are combined together to obtain a series of new memristor chaotic circuits by ingeniously utilizing the port characteristics of the device. A strange attractor, which is different from Chua's circuit, is generated, which enriches the content of memristor chaotic attractors.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TM132
本文编号：2220634
[Abstract]:The multi-scroll chaotic attractor has more key parameters and more complex dynamic characteristics than the traditional double-scroll chaotic attractor, so it is more suitable for chaotic secure communication. In the past twenty years, many researchers at home and abroad have explored the generation methods of multi-scroll chaotic attractor. The main problem of this kind of method is the complexity of mathematical calculation and the difficulty of circuit realization. Therefore, a simple method of multi-scroll realization is proposed to break the limitation of traditional methods in designing various kinds of complex nonlinear functions, which will lead to multi-scroll chaos. In recent years, the application of memristor, the fourth basic electronic element, to the design of chaotic circuits is a new direction of the development of chaotic circuits. Compared with traditional chaotic circuits, memristor chaotic circuits have more complex chaotic characteristics. With the application of chaotic theory in practical engineering more and more widely, how about It is of great practical significance to make better use of the nonlinearity of memristors to design all kinds of new memristor chaotic circuits. Focusing on the key problems in the practical application of chaos, the main work of this paper focuses on the generation method of multi-scroll chaotic attractors and the design of memristor chaotic circuits. The results are summarized as follows: (1) A chaotic multi-scroll realization method based on pulse control method is proposed. The method can realize the translation or expansion of the equilibrium point of the system and the generation of multi-scroll chaotic attractors by adding a suitable pulse source at a specific position in the dual-scroll chaotic system. A series of different multi-scroll and multi-wing butterfly chaotic attractors are generated in a unified and analog Lorenz system. Compared with the traditional methods, the new method does not need to construct the nonlinear control function of the system and to design complex implementation circuits. A method of system realization of compound chaotic attractor is proposed. Firstly, a unified chaotic system is constructed, that is, when the system parameters are different, the system can be decomposed into two subsystems, and two kinds of chaotic attractors can be obtained accordingly. Three different kinds of memristor chaotic circuits are designed and a series of different chaotic attractors are obtained. (3) The Chua's circuit is reformed and a five-order memristor is designed. Chaotic circuit. The dynamic characteristics of the system are studied by means of conventional dynamic analysis. A memristor simulator is designed with basic components, and the designed chaotic circuit is simulated by Pspice. The results of Pspice simulation are consistent with the theoretical analysis. (4) A new chaotic circuit is designed by using LC oscillator and magnetron memristor. The mechanical analysis shows that different phase trajectories such as double scroll, single scroll and periodic state can be produced by changing the circuit parameters. In order to control the chaos of the circuit, an analog time-delay feedback control circuit is designed. The simulation results of MATLAB show that the controller can realize the stable control of the proposed chaotic circuit. The chaotic attractor and the chaotic control phase diagram are observed in the waveguide. (5) A current feedback operational amplifier is selected as the active device, and four basic elements (resistance, capacitance, inductance, memristor) are combined together to obtain a series of new memristor chaotic circuits by ingeniously utilizing the port characteristics of the device. A strange attractor, which is different from Chua's circuit, is generated, which enriches the content of memristor chaotic attractors.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TM132
【参考文献】
相关期刊论文 前2条
1 ;Dynamics analysis of chaotic circuit with two memristors[J];Science China(Technological Sciences);2011年08期
2 包伯成;许建平;周国华;马正华;邹凌;;Chaotic memristive circuit:equivalent circuit realization and dynamical analysis[J];Chinese Physics B;2011年12期
，本文编号：2220634
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