Predictive dynamical and stochastic systems

TL;DR

This paper explores systems driven by future state predictions, revealing how prediction shaping and timing influence dynamics, and introduces the concept of predictive stochastic resonance where noise induces oscillations.

Contribution

It presents a general formalism for predictive dynamical systems and uncovers the phenomenon of noise-induced oscillations called predictive stochastic resonance.

Findings

Dynamics depend on prediction horizon and shaping.

Noise can induce oscillatory behavior.

Introduces predictive stochastic resonance phenomenon.

Abstract

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how far ahead in time to make them. We also report that noise can induce oscillatory behavior, which we call "predictive stochastic resonance".