Direct transition to high-dimensional chaos through a global bifurcationD. 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 ) 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