A Numerical Study of the Lorenz and Lorenz-Stenflo Systems

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.