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Direct transition to high-dimensional chaos through a global bifurcation

Pazó, Diego; Matías, Manuel A.
Europhysics Letters 72, 176-182 (2005)

In the present work we report on a genuine route by which a high-dimensional (with d>=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 in nite 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.