Anti-deterministic behaviour of discrete systems that are less predictable than noise

Abstract

We present a new type of deterministic dynamical behaviour that is less predictable than white noise. We call it anti-deterministic (AD) because time series corresponding to the dynamics of such systems do not generate deterministic lines in Recurrence Plots for small thresholds. We show that although the dynamics is chaotic in the sense of exponential divergence of nearby initial conditions and although some properties of AD data are similar to white noise, the AD dynamics is in fact less predictable than noise and hence is different from pseudo-random number generators.

Statistical independence in nonlinear maps coupled to non-invertible transformations

“…Chaotic systems have characteristics such as ergodicity, sensitive dependence on initial conditions and random-like behaviors, and thus they have attracted much attention for secure communication and cryptology. With researches of chaotic theories going more thorough, many works have focused on the construction of nonlinear dynamical models which can generate unpredictable sequences in the short term [41][42][43][44], etc. Refs.…”