Quenched noise and nonlinear oscillations in bistable multiscale systems

Technical University of Munich - Boltzmannstr. 3, 85748 Garching, Germany and Complexity Science Hub Vienna - Josefstädter Str. 39, 1080 Vienna, Austria

Received: 31 October 2017
Accepted: 24 November 2017

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 oscillators can be viewed as a new building block of nonlinear dynamics.