- Global bifurcations to strange attractors in a model for skewed varicose instability in thermal convection.
- Physica D
- Volume | Issue number
- 211 | 3-4
- Pages (from-to)
- Number of pages
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
We present a global bifurcation study of a four-dimensional system of differential equations, proposed by F.H. Busse and coworkers, modeling instabilities of convection rolls in the Rayleigh-Bénard experiment. The Rayleigh and Prandtl numbers are two natural parameters on which the system depends.
We focus on a detailed mathematical study, combining numerical pathfollowing and bifurcation analysis, of chaotic dynamics and transitions to chaotic dynamics. Numerical continuation makes clear how homoclinic and heteroclinic bifurcations organize the bifurcation diagram in the parameter plane. Combined with a theoretical bifurcation analysis this explains the development of patterns and the creation of chaotic spatio-temporal dynamics in the model. The organizing centers, such as heteroclinic cycles with resonance conditions among eigenvalues and homoclinic loops with geometric degeneracies (inclination flips), are identified and their unfoldings are analyzed. This ties the creation of strange attractors of various geometric structures to codimension-two global bifurcations.
Keywords: Global bifurcations; Strange attractors; Thermal convection model
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.