Unstable periodic orbits analysis in the generalized Lorenz-type system. (21st July 2020)

• Record Type: Journal Article
• Authors: Dong, Chengwei; Liu, Huihui; Li, Hantao
• Is Part Of: Journal of statistical mechanics. (2020:Jul.)
• Publication Date: 2020-07-21
• Subjects: nonlinear dynamics -- variational method -- generalized Lorenz-type system -- topological classification -- symbolic dynamics; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab9e5f
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: 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.