期刊
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
卷 2020, 期 7, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/ab9e5f
关键词
nonlinear dynamics; variational method; generalized Lorenz-type system; topological classification; symbolic dynamics
资金
- National Natural Science Foundation of China [11647085, 11647086]
- Shanxi Province Science Foundation for Youths [201901D211252]
- Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi [2019L0505, 2019L0554]
- Natural Science Research Fund of North University of China [XJJ201811]
In this paper, we investigated the unstable periodic orbits of a nonlinear chaotic generalized Lorenz-type system. By means of the variational method, appropriate symbolic dynamics are put forward, and the homotopy evolution approach, which can be used in the initialization of the cycle search, is introduced. Fourteen short unstable periodic orbits with different topological lengths, under specific parameter values, are calculated. We also explored the continuous deformation for part of the orbits while changing the parameter values,which provides a new approach to observe various bifurcations. The scale transformation of the generalized Lorenz-type system leads to a single parameter system known as the diffusionless Lorenz equations. By systematically calculating the periodic orbits in the diffusionless Lorenz equations, our research shows the efficiency of this topological classification method for the periodic solutions in the variants of a classical Lorenz system.
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