分数阶时滞忆阻混沌电路系统的动力学分析

发布时间：2018-03-16 07:14

本文选题：忆阻器　切入点：忆阻电路系统　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：忆阻器,也称记忆电阻器,是一种具有记忆功能特性的非线性元件,具有区别于其他三种电路基本元件(电阻器、电容器、电感器)无可比拟的特性,可以记忆经过它的电荷数量,也可以通过控制电流的动态变化改变其相应阻值,并且这种电流的变化特性在断电时可以继续保持,这就使得忆阻器在计算机工程、神经网络、电子工程、通信工程等领域有着非常广泛的应用。在非线性动力学领域,因为其作为新型非线性元件构成的电路表现出复杂的动力学现象,将传统混沌系统中的非线性元件用忆阻器代替可以构成一大类基于忆阻器的混沌电路系统。随着分数阶微积分的发展,同时考虑搭建电路存在延迟因子,因此将分数阶微积分理论引入到忆阻时滞系统模型中,然后对其分析这些系统复杂的动力学行为,特别是时滞和分数阶等参数对忆阻混沌系统的动力学行为影响,是一个值得研究的课题。并且,研究本课题对后期用来搭建混沌电路应用于信息安全、保密通信等领域,不仅具有重要的理论研究意义,还具有很好的实际应用前景。本文主要是基于忆阻器的发展应用,分数阶和时滞相关理论的发展应用,将这些理论结合并应用到忆阻器中来搭建混沌电路,提出了多种分数阶时滞忆阻模型系统;同时,应用稳定性理论分析系统的参数(时滞、分数阶和系统参数等)的稳定性区间,得到满足的多参数的Hopf分岔理论的横截条件;最后,具体分析多参数(时滞、分数阶和系统参数等)下的忆阻混沌系统的动力学行为。本文的创新点如下:(1)将常规时滞忆阻电路系统模型推广到分数阶系统,建立分数阶时滞忆阻电路混沌系统模型,使忆阻混沌系统能更加简洁规范的表现出来,揭示忆阻器混沌系统的本质特性。(2)利用李亚普罗夫稳定性定理,研究这些忆阻混沌系统基于时滞参数的平衡点稳定性的充分条件,得到时滞参数的稳定性区间,总结时滞和分数阶等参数对于系统稳定性的影响,同时给出对应参数的满足Hopf分岔的横截条件。(3)尝试分析系统的时滞、分数阶和系统参数等参数应用到忆阻混沌电路系统模型中对其动力学行为的影响。当系统时滞和分数阶等发生变化时,揭示分数阶时滞忆阻电路系统发生分岔、周期、混沌等复杂动力学行为的根本原因,并且可以得到在不同参数情况下产生混沌的最小阶数,为后期在保密通信应用提供广泛的应用前景。
[Abstract]:A memory resistor, also known as a memory resistor, is a kind of nonlinear element with memory characteristics, which is incomparable to the other three basic components of the circuit (resistors, capacitors, inductors). We can remember the amount of charge passing through it, or we can change the corresponding resistance by controlling the dynamic change of the current, and the characteristic of this current can be maintained when the power is off, which makes the amnesia in computer engineering, neural network. Electronic engineering, communication engineering and other fields have been widely used in the field of nonlinear dynamics, because of the complex dynamic phenomena in the circuits which are composed of new nonlinear components. A large class of chaotic circuit systems based on amnesia can be constructed by replacing the nonlinear elements in traditional chaotic systems with a resistor. With the development of fractional calculus, the delay factor of the circuit is considered at the same time. Therefore, the fractional calculus theory is introduced into the model of amnesia time-delay systems, and then the complex dynamic behaviors of these systems are analyzed, especially the effects of parameters such as delay and fractional order on the dynamical behavior of amnesia chaotic systems. It is worth studying. Moreover, this research is not only of great theoretical significance for the application of chaotic circuits to information security, secure communication and other fields, but also of great theoretical significance. This paper is mainly based on the development and application of memristors, fractional order and time-delay related theories, which are combined with these theories to build chaotic circuits. At the same time, stability theory is applied to analyze the stability interval of the system parameters (time delay, fractional order and system parameters, etc.), and the transversal conditions of the multi-parameter Hopf bifurcation theory are obtained. Finally, the dynamical behavior of the amnesia chaotic system with multiple parameters (time delay, fractional order and system parameters etc.) is analyzed in detail. The innovation of this paper is as follows: 1) the model of the conventional time-delay memory circuit system is extended to the fractional order system. The chaotic system model of fractional delay memory circuit is established, which makes the chaotic system more concise and canonical, and reveals the essential characteristics of the chaotic system. In this paper, the sufficient conditions for the stability of these amnesia chaotic systems based on the equilibrium point of the time-delay parameters are studied, the stability interval of the time-delay parameters is obtained, and the effects of the parameters such as time delay and fractional order on the stability of the system are summarized. At the same time, the transversal condition of corresponding parameters satisfying Hopf bifurcation is given. 3) the time-delay of the system is tried to be analyzed. The effects of parameters such as fractional order and system parameters on the dynamical behavior of the chaotic circuit system with amnesia are applied. When the delay and fractional order of the system change, it is revealed that the bifurcation and period occur in the fractional order delay circuit system. The fundamental cause of complex dynamical behavior such as chaos and the minimum order of chaos under different parameters can be obtained, which provides a broad application prospect for the later application of secure communication.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN60

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