The consequences of chaos as noise

We show that an archetypal nonlinear chaotic system can be interpreted as a first order anticausal IIR filter stimulated by i.i.d. Bernoulli noise. Based on this interpretation, we develop and characterize a number of estimators for the system, all of which perform poorly in high levels of noise. We hypothesize that when the noise-imposed channel capacity falls below the information production rate of the chaotic system no estimator can deduce the system´s underlying state. To provide direct evidence for this hypothesis, we compute the mutual information between the state and the corresponding noise-corrupted observations and demonstrate that at small signal-to-noise ratios the observations do not contain enough information about the state to accurately determine its value.