Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays

TL;DR

This paper presents an analytical method to predict and understand the emergence of specific spatiotemporal patterns in nonlinear oscillator networks with heterogeneous time delays, revealing how delays influence wave directions.

Contribution

The authors develop a novel analytical framework that links time delays to pattern formation in oscillator networks, extending to systems with diverse delay distributions.

Findings

Time delays influence the spectrum of the system's matrix.

Predicted wave patterns match simulations in Kuramoto networks.

The approach applies to systems with heterogeneous delays at finite scales.

Abstract

We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix associated to the system, leading to the emergence of waves with a preferred direction. We then create analytical predictions for the specific spatiotemporal patterns observed in individual simulations of time-delayed Kuramoto networks. This approach generalizes to systems with heterogeneous time delays at finite scales, which permits the study of spatiotemporal dynamics in a broad range of applications.