Locating Unstable Periodic Orbits in High-Dimensional Systems Using Subspace Fixed-Point Iteration(II)

Abstract

A numerical method is presented for efficiently detecting unstable periodic orbits embedded in chaotic attractors of high-dimensional differential-equation systems. This method locates fixed points of Poincaré maps using a form of fixed-point iteration that splits the phase space into appropriate subspaces. As an examle of high-dimensional systems, a model of a periodically driven semiconductor superlattice is analyzed.