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

TL;DR

This paper introduces anti-deterministic systems that exhibit less predictability than white noise, challenging traditional notions of chaos and randomness in dynamical systems.

Contribution

The paper defines and characterizes anti-deterministic behavior, demonstrating its distinct properties and unpredictability surpassing that of noise, with implications for understanding complex systems.

Findings

AD systems do not produce deterministic lines in Recurrence Plots.

AD dynamics are chaotic with exponential divergence of trajectories.

AD systems are less predictable than white 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.