Deterministic force-free resonant activation

TL;DR

This paper demonstrates a minimal, deterministic-force-free setup where noise-induced resonant effects, such as resonant activation and noise-enhanced stability, can occur depending on the modulation of noise stability.

Contribution

It introduces a novel, minimal setup without deterministic forces to observe noise-induced resonant phenomena in dynamical systems.

Findings

Resonant activation-like effects observed with periodic noise modulation.

Noise-enhanced-stability phenomena depending on initial modulation direction.

Demonstration of noise-induced effects without deterministic forces.

Abstract

Combined action of noise and deterministic force in dynamical systems can induce resonant effects. Here, we demonstrate a minimal, deterministic-force-free, setup allowing for occurrence of resonant, noise induced effects. We show that in the archetypal problem of escape from finite intervals driven by $\alpha$-stale noise with the periodically modulated stability index, depending on the initial direction of the modulation, resonant-activation-like or noise-enhanced-stability-like phenomena can be observed.