We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincar6 section map analysis, we propose a new approach for establishing one-dimensional sym...We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincar6 section map analysis, we propose a new approach for establishing one-dimensional symbolic dynamics based on the topological structure of the orbit. A newly designed variational method is stable numerically for cycle searching, and two orbital fragments can be used as basic building blocks for initialization. The topological classification based on the entire orbital structure is revealed to be effective. The deformation of periodic orbits with the change of parameters provides a chart to the periods of cycles. The current research may provide a methodology for finding and systematically classifying periodic orbits in other similar chaotic flows.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11647085,11647086,and 11747106)the Applied Basic Research Foundation of Shanxi Province,China(Grant No.201701D121011)the Natural Science Research Fund of North University of China(Grant No.XJJ2016036)
文摘We systematically investigate the periodic orbits of the Lorenz flow up to certain topological length. As an alternative to Poincar6 section map analysis, we propose a new approach for establishing one-dimensional symbolic dynamics based on the topological structure of the orbit. A newly designed variational method is stable numerically for cycle searching, and two orbital fragments can be used as basic building blocks for initialization. The topological classification based on the entire orbital structure is revealed to be effective. The deformation of periodic orbits with the change of parameters provides a chart to the periods of cycles. The current research may provide a methodology for finding and systematically classifying periodic orbits in other similar chaotic flows.
