Quenched Noise and Nonlinear Oscillations in Bistable Multiscale Systems

TL;DR

This paper investigates the effects of quenched noise on nonlinear oscillators, revealing new phenomena like period shifts and quenched resonance, and introduces a novel theoretical framework for these systems.

Contribution

It provides the first analytical and numerical study of quenched noise in nonlinear oscillators, expanding understanding beyond traditional annealed noise models.

Findings

Identification of period shifts due to quenched noise

Discovery of new trapped oscillation types

Observation of quenched resonance phenomena

Abstract

Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic setting. Yet, there is no theory regarding the quenched noise scenario of random parameters sampled on fixed time intervals, although this situation is often a lot more natural. Here we study a paradigmatic nonlinear oscillator of van-der-Pol/FitzHugh-Nagumo type under quenched noise as a piecewise-deterministic Markov process. There are several interesting effects such as period shifts and new different trapped types of small-amplitude oscillations, which can be captured analytically. Furthermore, we numerically discover quenched resonance and show that it differs significantly from previous finite-noise optimality resonance effects. This demonstrates that quenched oscillatorscan be viewed as a new building block of nonlinear dynamics.