# Asymmetric noise-induced large fluctuations in coupled systems

## TL;DR

This paper investigates how noise in one coupled system can induce large fluctuations in another, even when the second system is noise-free, revealing complex behaviors driven by coupling and noise transmission.

## Contribution

It introduces a generic model demonstrating how noise in one subsystem causes large fluctuations in a coupled, noise-free system, with quantitative analysis of switching time scales and probabilities.

## Key findings

- Noise in one system transmits through coupling to induce large fluctuations.
- Switching probability scales inversely with the square of noise amplitude.
- Simulation results agree with analytical predictions.

## Abstract

Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, epidemiology to engineering and robotics. In the presence of noise and uncertainty, inter- actions between the individual components can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems, and show how noise in one part of the system is transmitted through the coupling interface. Working synergistically with the coupling, the noise on one system drives a large fluctuation in the other, even when there is no noise in the second system. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. Uncertainty effects are quantified by showing how characteristic time scales of noise induced switching scale as a function of the coupling between the two coupled parts of the experiment. In addition, our results show that the probability of switching in the noise-free system scales inversely as the square of reduced noise intensity amplitude, rendering the virtual probability of switching to be an extremely rare event. Our results showing the interplay between transmitted noise and coupling are also confirmed through simulations, which agree quite well with analytic theory.