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Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system.
- Source :
- Chaos; Sep2013, Vol. 23 Issue 3, p033108-033108-6, 1p
- Publication Year :
- 2013
-
Abstract
- In this paper, we show, by means of a linear scaling in time and coordinates, that the Chen system, given by x=a(y-x), y=(c-a)x+cy-xz, ż=-bz+xy, is, generically (c≠0), a special case of the Lorenz system. First, we infer that it is enough to consider two parameters to study its dynamics. Furthermore, we prove that there exists a homothetic transformation between the Chen and the Lorenz systems and, accordingly, all the dynamical behavior exhibited by the Chen system is present in the Lorenz system (since the former is a special case of the second). We illustrate our results relating Hopf bifurcations, periodic orbits, invariant surfaces, and chaotic attractors of both systems. Since there has been a large literature that has ignored this equivalence, the aim of this paper is to review and clarify this field. Unfortunately, a lot of the previous papers on the Chen system are unnecessary or incorrect. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10541500
- Volume :
- 23
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Chaos
- Publication Type :
- Academic Journal
- Accession number :
- 90480487
- Full Text :
- https://doi.org/10.1063/1.4813227