lorenz attractor การใช้

• Some of the topics covered in the magazine listings included fractal trees, Lorenz attractors and functions.
• This attractor has some similarities to the Lorenz attractor, but is simpler and has only one manifold.
• Examples of strange attractors include the H閚on attractor, R鰏sler attractor, Tamari attractor, and the Lorenz attractor.
• For example, look at the picture of the Lorenz attractor at the top of the Lorenz system article.
• The original R鰏sler paper states the R鰏sler attractor was intended to behave similarly to the Lorenz attractor, but also be easier to analyze qualitatively.
• There are things like the Lorenz attractor, which while flipping between two usual positions, is not an oscillation because its timing is unpredictable.
• The Lorenz attractor is difficult to analyze, but the action of the differential equation on the attractor is described by a fairly simple geometric model.
• :Is the Lorenz attractor ( oops, 3D ) Smale horseshoe not the most famous one ? talk ) 09 : 46, 28 July 2009 ( UTC)
• Tucker obtained his Ph . D . in 1998 at Uppsala University ( thesis : " The Lorenz attractor exists " ) with Lennart Carleson as advisor.
• Such equations can only be solved exactly if they happen to have some other simplifying property, for instance chaotic behavior such as the Lorenz attractor and the R鰏sler attractor.
• Lorenz's discovery, which gave its name to Lorenz attractors, showed that even detailed atmospheric modelling cannot, in general, make precise long-term weather predictions.
• The "'Lorenz attractor "'is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its butterfly shape.
• Because of the topological transitivity condition, this is likely to produce a picture of the entire final attractor, and indeed both orbits shown in the figure on the right give a picture of the general shape of the Lorenz attractor.
• Higher-order differential equations may have simpler conditions for chaos ( I don't know ), but the Lorenz attractor equations are first-order, and that is a situation in nature where " all hell breaks loose ".
• In fact, certain well-known chaotic systems, such as the Lorenz attractor and the R鰏sler map, are conventionally described as a system of three first-order differential equations that can combine into a single ( although rather complicated ) jerk equation.
• If I'm estimating the K-S entropies of a logistic map, or a Lorenz attractor, then I'm calculating how a family of general measures of diversity ( the Renyi entropies ) of the possible histories of the trajectory increase with time.
• Lorenz went on to explore the underlying mathematics and published his conclusions in a seminal work titled " Deterministic Nonperiodic Flow ", in which he described a relatively simple system of equations that resulted in a very complicated dynamical object now known as the Lorenz attractor.
• The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because it was not only one of the first, but it is also one of the most complex and as such gives rise to a very interesting pattern, that with a little imagination, looks like the wings of a butterfly.
• The "'Lorenz attractor "', introduced by Edward Lorenz in 1963, is a non-linear three-dimensional deterministic dynamical system derived from the simplified equations of convection rolls arising in the dynamical equations of the chaotic behavior and displays what is today called a strange attractor; this was proven by W . Tucker in 2001.