Computing fractal dimension in supertransient systems directly, rapidly and reliablyR. Breban1 and H. E. Nusse2
1 Semel Institute for Neuroscience and Human Behavior, University of California Los Angeles, CA 90024, USA
2 University of Groningen, Department of Econometrics - P.O. Box 800 NL-9700 AV, Groningen, The Netherlands
received 24 June 2006; accepted in final form 31 October 2006
published online 29 November 2006
Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles have a big impact on laboratory measurements, and it is important to compute the dimension of such stable sets including fractal basin boundaries through a direct method. In this work, we present a new method to compute the dimension of stable sets of chaotic saddles directly, rapidly and reliably.
05.45.-a - Nonlinear dynamics and chaos.
05.45.Df - Fractals.
05.45.Pq - Numerical simulations of chaotic systems.
© EDP Sciences 2006