Journal
JOURNAL OF THE KOREAN PHYSICAL SOCIETY
Volume 75, Issue 3, Pages 188-195Publisher
KOREAN PHYSICAL SOC
DOI: 10.3938/jkps.75.188
Keywords
Chen system; Lu system; Variational method; Periodic orbit
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Funding
- National Natural Science Foundation of China [11647085, 11647086, 11747106]
- Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi [2019L0505]
- Applied Basic Research Foundation of Shanxi Province, China [201701D121011]
- Natural Science Research Fund of North University of China [XJJ2016 036, XJJ201811]
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In this research, we systematically investigated the organization of the unstable cycles for the Chen and the Lu systems. The multivalued and non-invertible return maps show the complexity of the two dissipative flows, and a new designed method for building one-dimensional symbolic dynamics based on the orbital topological structure is proposed. We employed the variational approach for the calculations of unstable periodic orbits and used two orbital fragments for initialization. The homotopy evolution of periodic orbits provides evolution rules for the periods. For a chaotic flow, current work supplies an interesting framework for a chart of periodic orbits.
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