منابع مشابه
The Lorenz Attractor Exists
We prove that the Lorenz equations support a strange attractor, as conjectured by Ed-ward Lorenz in 1963. We also prove that the attractor is robust, i.e., it persists under small perturbations of the coeecients in the underlying diierential equations. The proof is based on a combination of normal form theory and rigorous numerical computations.
متن کاملThe Lorenz Attractor Exists – An Auto-Validated Proof
We present an algorithm for computing rigorous solutions to a large class of ordinary differential equations. The main algorithm is based on a partitioning process and the use of interval arithmetic with directed rounding. As an application, we prove that the Lorenz equations support a strange attractor, as conjectured by Edward Lorenz in 1963. This conjecture was recently listed by Steven Smal...
متن کاملChen's Attractor Exists
By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši’lnikov type that connects two nontrivial singular points. The Ši’lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists on...
متن کاملThe Lorenz Attractor Is Mixing
We study a class of geometric Lorenz flows, introduced independently by Afrăımovič, Bykov & Sil′nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. As a consequence, we show that the classical Lorenz attractor is mixing.
متن کاملSimplifications of the Lorenz attractor.
The Lorenz attractor was once thought to be the mathematically simplest autonomous dissipative chaotic flow, but it is now known that it is only one member of a very large family of such systems, many of which are even simpler. Even the system originally proposed by Lorenz is not in its simplest possible form. This paper will describe a number of simplifications that can be made to the Lorenz s...
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ژورنال
عنوان ژورنال: Nature
سال: 2000
ISSN: 0028-0836,1476-4687
DOI: 10.1038/35023206