Two paradigmatic scenarios for inverse stochastic resonance

TL;DR

This paper identifies two fundamental mechanisms behind inverse stochastic resonance in coupled stochastic active rotators, explaining how noise influences oscillatory behavior near bifurcation points through slow-fast dynamics.

Contribution

It introduces two generic scenarios for inverse stochastic resonance, linking noise effects to bifurcation dynamics in coupled active rotator models.

Findings

Inverse stochastic resonance occurs via switching between states in excitable regimes.

Resonance arises from noise-enhanced stability of unstable fixed points.

Mechanisms are explained through slow-fast analysis of noiseless systems.

Abstract

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated with a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow-fast analysis of the corresponding noiseless systems.