Recognizing randomness in a time series

Abstract

We study the effects of intrinsic noise on low-dimensional chaotic systems and nonlinear oscillating systems. For the former, we show that adding increasing amounts of intrinsic noise increasingly destroys the characteristic short-term predictability of chaos, while for the latter, we show that phase points near the deterministic limit cycle execute Brownian-like motions. Quantitative methods are also proposed to estimate the amount of noise contained in the signal.