设计和实现三维空间任意庞加莱截平面电路  

Design and implementation of an arbitrary poincare plane section circuit in three-dimensional space

作　　者：陈红[1] 吴玲 

机构地区：[1]黑龙江大学电子工程学院,哈尔滨150080

出　　处：《物理学报》2013年第2期113-122,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61072072);黑龙江省自然科学基金(批准号:F201249);黑龙江省教育厅科研项目(批准号:12521402);黑龙江省普通高等学校电子工程重点实验室(批准号:DZZD20100021)资助的课题~~

摘　　要：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.The Poincare section method is an effective method to simplify the analysis of complex dynamic system motion state. To achieve online observing system states conveniently, an arbitrary directional Poincare plane section physical electronic circuit in three- dimensional space is designed and realized. Firstly, the key problems of an arbitrary Poincare plane section circuit design are analyzed and studied in detail. And then the physical circuit is realized in classification. As Chua＇s circuit has rich dynamic behaviors, the typical Chua＇s circuit is chosen as the experimental dynamical system. And then a lot of the physical experiments with this Poincare plane section circuit are performed in real time. For example, Poincare plane section diagrams in different conditions of Chua＇s circuit are measured, and the test experiments in the same kind of chaotic state, with different plane sections chosen, are carried out. All Poincare section map diagrams and phase diagrams are measured by two double-channel oscilloscopes （analogue oscilloscope and digital oscilloscope）. At the same time, computer simulation experiments are conducted by using Matlab. These results show the practicability and effectiveness of the Poincare plane section circuit.

关 键 词：庞加莱截面 截平面电路 蔡氏电路 示波器 

分 类 号：TN710[电子电信—电路与系统]