Exploiting deterministic features in apparently stochastic data

Scientific Reports. 2022. Vol. 12. No. 1. Article 19843.

Stoop R., Orlando G., Bufalo M., Rossa F. D.

Many processes in nature are the result of many coupled individual subsystems (like population
dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the
past science has mostly focused on. Often, these systems are characterized by bursts of seemingly
stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong
deterministic ingredient is often obscured by the stochastic features. We test this by modeling
classically stochastic considered real-world data from both, the stochastic as well as the deterministic
approaches to find that the deterministic approach’s results level with those from the stochastic side.
Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which
can be exploited for steering the dynamics into a desired regime.

Keywords: Android, Determinism in Economics, Rulkov map, nonlinear stochastic processes, ARIMA-GARCH