Discriminating additive from dynamical noise for chaotic time series

Abstract

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only for one variable of the system, while the noise corrupting the second variable is still Gaussian distributed independent of distribution of dynamical noise. Based on these results and using scaling properties of the correlation entropy, we propose a simple method of discriminating additive from dynamical noise. This approach is also useful for estimation of noise level for chaotic time series. We show that the proposed method works well in a wide range of noise levels, providing that one kind of noise predominates and we analyze the variable of the system for which the contamination follows Cauchy-like distribution in the presence of dynamical noise.