Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 16: Fluid dynamics I
DY 16.8: Talk
Wednesday, March 25, 2009, 16:45–17:00, ZEU 255
Basin boundary, edge of chaos and edge state in a two-dimensional model — •Jürgen Vollmer1,2, Tobias Schneider2, and Bruno Eckhardt2 — 1Dept. Dynamics of Complex Fluids, MPI for Dynamics & Self-Organization, 37073 Göttingen, Germany — 2FB Physik, Philipps Univ. Marburg, 35032 Marburg, Germany
Basin boundaries are the boundaries between the basins of attraction of coexisting attractors. When one of the attractors breaks up and becomes a transient repelling structure also the basin boundary disappears. Nevertheless, it is possible to distinguish the two types of dynamics in phase space and to define and identify a remnant of the basin boundary, the edge of chaos. We here demonstrate the concept using a two-dimensional (2D) map, and discuss properties of the edge of chaos and its invariant subspaces, the edge states. The discussion is motivated and guided by observations on certain shear flows like pipe flow and plane Couette flow where the laminar profile and a transient turbulent dynamics coexist for certain parameters, and where the notions edge of chaos and edge states proved to be useful concepts to characterize the transition to chaos. The 2D map captures many of the features identified in laboratory experiments and direct numerical simulations of hydrodynamic flows.