Analysis of chaotic saddles in low-dimensional dynamical systems: the derivative nonlinear Schrodinger equation

摘要

In this paper, we present a computational study of nonattracting chaotic sets known as chaotic saddles in a low-dimensional dynamical system describing stationary solutions of the derivative nonlinear Schrodinger equation, a driven-dissipative model for Alfven waves. These chaotic saddles have "gaps" which are filled at chaotic transitions, such as a saddle-node bifurcation and an interior crisis. We give a detailed explanation of how to numerically determine the chaotic saddles, and describe how a chaotic attractor after an interior crisis point can be "decomposed" into two chaotic saddles, dynamically connected by a set of coupling unstable periodic orbits created by a gap filling "explosion" after the crisis. This coupling between two chaotic saddles is responsible for the intermittent dynamics displayed by the chaotic system after the interior crisis. (C) 2004 Elsevier B.V. All rights reserved.