Detecting the unstable periodic orbits of chaotic nonautonomous systems with an approximate global Poincare map

This Letter presents a simple approach that detects unstable periodic orbit s embedded in a chaotic motion of an unknown nonautonomous system with nois y perturbation. An identification technique is developed to obtain the mode l of the unknown system. The nonautonomous system is approximated by a diff erence system and then a global Poincare map function is derived from the d ifference system. The unstable periodic orbits can be detected via the map function. The proposed method is both accurate and feasible as demonstrated by two chaotic nonautonomous systems. (C) 2001 Published by Elsevier Scien ce B.V.