A Numerical Study of the Lorenz and Lorenz-Stenflo Systems
2005 (English)Doctoral thesis, monograph (Other scientific)
In 1998 the Swedish mathematician Warwick Tucker used rigorous interval arithmetic and normal form theory to prove the existence of a strange attractor in the Lorenz system. In large parts, that proof consists of computations implemented and performed on a computer. This thesis is an independent numerical verification of the result obtained by Warwick Tucker, as well as a study of a higher-dimensional system of ordinary differential equations introduced by the Swedish physicist Lennart Stenflo.
The same type of mapping data as Warwick Tucker obtained is calculated here via a combination of numerical integration, solving optimisation problems and a coordinate change that brings the system to a normal form around the stationary point in the origin. This data is collected in a graph and the problem of determining the existence of a strange attractor is translated to a few graph theoretical problems. The end result, after the numerical study, is a support for the conclusion that the attractor set of the Lorenz system is a strange attractor and also for the conclusion that the Lorenz-Stenflo system possesses a strange attractor.
Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , vii, 144 p.
Mathematics, Warwick Tucker, Strange attractor, Lorenz equations, Lorenz-Stenflo equations, Lorenz attractor, Lorenz-Stenflo attractor, Dynamical systems, Normal form theory
IdentifiersURN: urn:nbn:se:kth:diva-172ISBN: 91-7283-997-XOAI: oai:DiVA.org:kth-172DiVA: diva2:7678
2005-04-22, M3, Brinellvägen 64, KTH, 09:00
QC 201010072005-04-182005-04-182010-10-07Bibliographically approved