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

Abstract

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.