Visualizing the transition to chaos in the Lorenz system

HM Osinga, B Krauskopf, E.J. Doedel

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)


The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This paper addresses the role of the global stable and unstable manifolds in organising the dynamics. More precisely, for the standard system parameters, the origin has a two-dimensional stable manifold and the other two equilibria each have a two-dimensional unstable manifold. The intersections of these manifolds in the three-dimensional phase space form heteroclinic connections from the nontrivial equilibria to the origin. A parameter-dependent visualization of these manifolds clarifies the transition to chaos in the Lorenz system
Translated title of the contributionVisualizing the transition to chaos in the Lorenz system
Original languageEnglish
Title of host publicationTopology-Based Methods in Visualization 2007
Publication statusPublished - Nov 2006

Bibliographical note

Name and Venue of Event: Grimma, Germany


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