动力学变换法探测连续系统不稳定周期轨道  

Detecting unstable periodic orbits from continuous chaotic dynamical systems by dynamical transformation method

作　　者：马文聪[1] 金宁德[1] 高忠科[1] 

机构地区：[1]天津大学电气与自动化工程学院,天津300072

出　　处：《物理学报》2012年第17期119-127,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:50974095;41174109;61104148)资助的课题~~

摘　　要：本文利用动力学变换方法和庞加莱截面方法对两种连续混沌动力学系统进行不稳定周期轨道探测研究,并对Lorenz系统进行了替代数据法检验.结果表明:基于庞加莱截面的动力学变换改进算法可有效探测连续混沌动力学系统中的不稳定周期轨道.Detecting unstable periodic orbits （UPOs） from chaotic dynamic systems is a challenging problem. For a large number of complex systems, we can collect some experimental time series data but cannot find theoretical models to describe them. Thus, detecting unstable periodic orbits from experimental data can help us understand the chaotic properties of physical phenomenon without using theoretical models. We, in this paper, first use the dynamical transformation （DT） algorithm to detect unstable periodic orbits from chaotic systems, and find that the original DT algorithm can detect the UPOs from the time series of chaotic discrete map, but it is infeasible for the time series from continuous chaotic flow. In this regard, we then propose an improved DT algorithm that is based on the Poincare section method to detect the UPOs from continuous chaotic flow. In particular, we transform the continuous flow data into discrete map time series in terms of Poincare section, and then detect unstable periodic orbits from the transformed discrete map time series. In addition, we take RSssler and Lorenz chaotic systems as examples to demonstrate the effectiveness of our proposed method.

关 键 词：不稳定周期轨道 动力学变换 连续混沌动力系统 庞加莱截面 

分 类 号：O415.5[理学—理论物理]