中文摘要：

为解决用示波器观测单变量非线性系统难的问题，本文提出了一种45°线法，该方法能将随时间变化的连续信号以特殊的方式转换成直角坐标上45°线上的点图，并可用通用双踪示波器（模拟或数字均可）直接显示出来，从而达到直接方便地观测和分析单变量被测系统运行时的各种状态，如周期稳定态，局部和全局不稳定态．文中详细阐述了该方法的机理．同时，研究和解决了设计实现该方法物理电路的关键问题，即从连续变化的信号中提取出能反映系统状态的有用信号．由于蔡氏电路是典型的非线性系统，且能随参数的变化产生各种丰富的状态，本文选用该电路作为被测系统进行了大量的物理实验，实验结果证实了该方法的有效性和实用性．

英文摘要：

In order to solve the problem why it was hard to observe the single-variable nonlinear system, this article proposed the 45° line method. In this method, the continuous signal changing with time was transformed into dots on the 45° line of the rectangular coordinates, so that it could be directly displayed on a general dual-trace oscilloscope （either analog or digital）. In this way, it is convenient to directly observe and analyze various states of single-variable system while the system is running, such as the periodical stable states, the local and global non-stable states. The mechanism of this method was expounded in this paper. In addition, the key issues in physical circuit design and implementation of this method were researched and solved, i.e., the useful signal which reflected the state of the system could be extracted from the continuously changing signal. Since the Chua＇s circuit is a typical nonlinear system, and it could produce abundant states with variation of parameters, so it was chosen as the system under test to conduct a great number of physical experiments. The experimental results confirmed the effectiveness and practicability of this method.