Study on the Application of Poincaré Section Algorithm to Chaotic Vibration Identification

作者: 刘树勇 * , 朱石坚 , 杨庆超 , 杨爱波 :;

关键词: Poincaré截面轨道簇混沌Poincaré Section Orbits Cluster Chaos



Abstract: In the process of Poincaré section extraction for chaotic vibration identification, there are many problems such as selection of the Poincaré section location on the phase space attractor reconstructed from single variable time series, determination of these sections when the system under quasi-periodic excitations, should be solved effectively. The improved Poincaré section is presented in this paper. The main idea is to consider these points which are satisfied with the neighborhood condition as the same section points, and a bunch of experimental trajectories which are derived from the signals are normalized. The simulation and experiment results show that when the cluster orbits of experimental attractor occur and the system is excited with different frequencies, the improved method is applied to determine the Poincaré section correctly. The interested phenomenon including multi-periodic behavior, chaos, and quasi-periodic vibration section are observed.

文章引用: 刘树勇 , 朱石坚 , 杨庆超 , 杨爱波 (2011) Poincaré截面法在混沌振动识别中的应用研究。 应用物理, 1, 108-115. doi: 10.12677/app.2011.13018


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