Reliability of Coupled Oscillators II: Larger Networks

TL;DR

This paper investigates the reliability of larger phase oscillator networks to fluctuating inputs, extending previous two-cell network results, analyzing chaos, and localizing unreliability sources within modular, acyclic networks.

Contribution

It extends reliability analysis from two-cell to larger networks, providing methods to identify unreliability sources and understand propagation in modular systems.

Findings

Chaos can occur in the absence of inputs in larger networks.

Reliability can be analyzed through network decomposition into modules.

Unreliability sources can be localized within the network structure.

Abstract

We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In this paper, we extend previous results on two-cell networks to larger systems. The first issue that arises is chaos in the absence of inputs, which we demonstrate and interpret in terms of reliability. We give a mathematical analysis of networks that can be decomposed into modules connected by an acyclic graph. For this class of networks, we show how to localize the source of unreliability, and address questions concerning downstream propagation of unreliability once it is produced.