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

This Letter presents a simple approach that detects unstable periodic orbits embedded in a chaotic motion of an unknown nonautonomous system with noisy perturbation. An identification technique is developed to obtain the model of the unknown system. The nonautonomous system is approximated by a difference system and then a global Poincaré map function is derived from the difference 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.