# The infinitely many zeros of stochastic coupled oscillators driven by random forces

## TL;DR

This paper extends the study of zeros in stochastic oscillators to coupled systems, analyzing harmonic and nonlinear cases, and evaluates numerical methods for capturing this oscillatory behavior.

## Contribution

It introduces the analysis of infinitely many zeros in coupled stochastic oscillators, including harmonic and nonlinear types, and assesses numerical integrators for these dynamics.

## Key findings

- Coupled harmonic oscillators exhibit infinitely many zeros under random forces.
- Certain classes of nonlinear oscillators also show this oscillatory behavior.
- Numerical integrators can effectively reproduce the zeros in these stochastic systems.

## Abstract

In this work, previous results concerning the infinitely many zeros of single stochastic oscillators driven by random forces are extended to the general class of coupled stochastic oscillators. We focus on three main subjects: 1) the analysis of this oscillatory behavior for the case of coupled harmonic oscillators; 2) the identification of some classes of coupled nonlinear oscillators showing this oscillatory dynamics and 3) the capability of some numerical integrators - thought as discrete dynamical systems - for reproducing the infinitely many zeros of coupled harmonic oscillators driven by random forces.