Chaos in driven Alfvén systems : unstable periodic orbits and chaotic saddles Article - Janvier 2007

A. C.-L. Chian, W. M. Santana, E. L. Rempel, F. A. Borotto, T. Hada, Y. Kamide

A. C.-L. Chian, W. M. Santana, E. L. Rempel, F. A. Borotto, T. Hada, Y. Kamide, « Chaos in driven Alfvén systems : unstable periodic orbits and chaotic saddles  », Nonlinear Processes in Geophysics, janvier 2007, pp. 17-29. ISSN 1023-5809

Abstract

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

Voir la notice complète sur HAL

Actualités