Europhys. Lett.
Volume 72, Number 2, October 2005
Page(s) 176 - 182
Section General
Published online 21 September 2005
Europhys. Lett., 72 (2), pp. 176-182 (2005)
DOI: 10.1209/epl/i2005-10239-3

Direct transition to high-dimensional chaos through a global bifurcation

D. Pazó1 and M. A. Matías2

1  Grupo de Física Non Lineal, Facultade de Física Universidade de Santiago de Compostela - E-15782 Santiago de Compostela, Spain
2  Instituto Mediterráneo de Estudios Avanzados, IMEDEA (CSIC-UIB) E-07122 Palma de Mallorca, Spain

received 4 July 2005; accepted in final form 1 September 2005
published online 21 September 2005

In the present work we report on a genuine route by which a high-dimensional (with $d\gtrsim 4$) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step. The high-dimensional chaotic set is created in a heteroclinic global bifurcation that yields an infinite number of unstable tori. The mechanism is illustrated using a system constructed by coupling three Lorenz oscillators. So, the route presented here can be considered a prototype for high-dimensional chaotic behavior just as the Lorenz model is for low-dimensional chaos.

05.45.Jn - High-dimensional chaos.
05.45.Xt - Synchronization; coupled oscillators.

© EDP Sciences 2005