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庞加莱截面法是简化分析复杂动力系统运动状态的有效方法.为实现在线方便观测复杂系统的状态,本文设计并实现了三维任意庞加莱截平面电子电路.文章首先详细分析和研究了设计三维任意庞加莱截平面电路的关键性问题,然后分类设计和实现了物理电路.由于蔡氏电路具有丰富的动力学行为,因此以典型的蔡氏电路作为实验待测动力系统,对设计的截平面电路进行了大量的物理实验,测出了蔡氏电路各种状态下的截平面图,以及同一种混沌状态下选取不同截面的测试实验.实验中采用了两种双踪示波器(模拟示波器和数字示波器)在线实测了庞加莱截平面映射和状态图.与此同时,利用Matlab进行了计算机仿真辅助实验.所有实验结果表明设计的庞加莱截平面电路具有实用性和有效性.
Poincaré section method is an effective way to simplify the analysis of complex dynamic state of dynamic system.In order to realize the state of complex system easily observed on line, this paper designs and realizes a three-dimensional arbitrary Poincaré sectioned electronic circuit.Firstly, the article analyzes and studies design Dimensional arbitrary Poincaré cut-flat circuit, and then classify the design and realization of the physical circuit.As the Chua’s circuit has a wealth of dynamic behavior, with typical Chua’s circuit as the test power system to be tested, the design of the cutting plane A large number of physical experiments were carried out in the circuit, and the cross-sectional plan of the Chua’s circuit in various states and the test of different cross-sections in the same chaotic state were measured. Two types of dual-track oscilloscopes (analog oscilloscope and digital oscilloscope) The Poincaré section plane mapping and state diagram were measured online.At the same time, the simulation experiment was carried out by using Matlab.All the experimental results show that the Poincare sectional plane circuit is practical and effective.