忆阻Lorenz混沌电路及其变时刻脉冲控制

发布时间：2018-06-15 23:47

本文选题：Lorenz系统 + 忆阻器　；参考：《西南大学》2017年硕士论文

【摘要】：混沌作为自然科学和社会科学中广泛存在的一种现象,也作为非线性领域内一种特殊情况,引起了国内外学者的广泛关注。目前为止研究混沌的一种广泛和有效的手段是通过电路进行研究。同时,由于忆阻器的非线性特性,以忆阻器作为非线性元件设计混沌电路也逐渐得到研究人员的关注。现阶段,忆阻混沌电路的设计主要是基于蔡氏电路,采用不同类型忆阻器模型替换蔡氏电路中的非线性电阻。在对混沌电路进行脉冲控制时,主要的研究方案是固定时刻脉冲控制。对忆阻混沌电路的设计和脉冲控制还可作如下考虑:首先,我们可以尝试挖掘蔡氏电路之外的忆阻混沌电路结构;其次,在脉冲控制方案中,变时刻脉冲控制也值得我们进行研究和探讨。本文以忆阻器和Lorenz系统为基础,提出了一种新的忆阻Lorenz电路,并进一步研究了忆阻Lorenz电路的特点以及此电路系统在变时刻脉冲控制下的稳定性分析。具体的研究内容和创新之处如下:1.基于二次型忆阻器模型,采用简单的电路器件,搭建了二次型忆阻器的电路模型,并将此电路模型应用到Lorenz系统中,组建了忆阻Lorenz电路,基于电路,分析忆阻Lorenz系统的动力学行为和混沌现象。2.基于Lyapunov稳定性理论,采用脉冲控制的原理,设计了一种变时刻脉冲控制器,实现了对忆阻Lorenz混沌系统的控制。在证明此控制方法有效性的过程中,通过B-equivalence条件和比较系统的方法,证明了系统在变时刻脉冲控制下与在固定时刻脉冲控制下具有相同的稳定性,以此将变时刻脉冲问题转化成固定时刻脉冲问题。通过证明系统在固定时刻脉冲控制下达到稳定状态,实现了变时刻脉冲控制忆阻Lorenz混沌系统,并通过数值仿真进行了验证。
[Abstract]:Chaos, as a widespread phenomenon in natural science and social science, is also a special case in nonlinear field, which has attracted the attention of scholars both at home and abroad. So far, one of the most effective ways to study chaos is by circuit. At the same time, because of the nonlinear characteristics of the resistive device, the design of chaotic circuit using the resistor as a nonlinear element has gradually attracted the attention of researchers. At present, the design of amnesia chaotic circuit is mainly based on Chua's circuit. Different types of amnesia models are used to replace the nonlinear resistor in Chua's circuit. In the pulse control of chaotic circuit, the main research scheme is fixed time pulse control. The design and pulse control of amnesia chaotic circuit can also be considered as follows: first, we can try to excavate the structure of amnesia chaotic circuit other than Chua's circuit; secondly, in the pulse control scheme, Variable time pulse control is also worth our research and discussion. In this paper, a new type of amnesia Lorenz circuit is proposed based on the resistive device and Lorenz system. The characteristics of the circuit and the stability analysis of the circuit system under the variable time pulse control are further studied. The specific research contents and innovations are as follows: 1. Based on the model of quadratic type amnesia, the circuit model of quadratic type amnesia is built by using simple circuit device. The circuit model is applied to Lorenz system, and the circuit of amnesia Lorenz is constructed, which is based on circuit. The dynamical behavior and chaotic phenomena of Lorenz system are analyzed. Based on Lyapunov stability theory and the principle of pulse control, a variable time pulse controller is designed to control Lorenz chaotic system. In the process of proving the effectiveness of this control method, it is proved that the system has the same stability under the variable time pulse control and the fixed time pulse control through the B-equivalence condition and the comparison system method. In this way, the variable time pulse problem is transformed into the fixed time pulse problem. It is proved that the system is stable under the control of pulse at fixed time, and the Lorenz chaotic system is controlled by variable time pulse, and verified by numerical simulation.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN60

【参考文献】