Symbolic dynamics and periodic orbits of the Lorenz attractor*
نویسندگان
چکیده
منابع مشابه
Symbolic dynamics and periodic orbits of the Lorenz attractor*
The butterfly-like Lorenz attractor is one of the best known images of chaos. The computations in this paper exploit symbolic dynamics and other basic notions of hyperbolicity theory to take apart the Lorenz attractor using periodic orbits. We compute all 111011 periodic orbits corresponding to symbol sequences of length 20 or less, periodic orbits whose symbol sequences have hundreds of symbol...
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We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computatio...
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Numerical method for detection of unstable periodic orbits on attractors of nonlinear dynamical systems is proposed. This method requires the similar techniques as the data assimilation does. This fact facilitates its implementation for geophysical models. Some low-period orbits of the Lorenz model have been calculated explicitely. The orbits encoding and application of symbolic dynamics is use...
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Recent progress of symbolic dynamics of oneand especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is capable to yield global results on chaotic and periodic regimes in systems of dissipative ODEs which cannot be obtained neither by purely analytical means nor...
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Controlling chaos has become a challenging topic in nonlinear dynamics. It has been studied in many scientific and engineering fields such as physics, chemistry, electrical circuit, etc., and several extension and applications of the original OGY control method [1] have been reported [2–6]. Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [7]. Recent r...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2003
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/16/3/314