Analytical approximations for the speed of pacemaker-generated waves

TL;DR

This paper uses analytical methods to study how various factors influence the speed of pacemaker-generated waves in oscillatory media, relevant to chemical and biological systems, and compares estimates with numerical simulations.

Contribution

It introduces analytical approaches to determine wave speed in oscillatory systems with negative feedback, considering effects of timescale separation, size, and frequency of pacemakers.

Findings

Analytical estimates align well with numerical simulations.

Timescale separation significantly affects wave speed.

Size and frequency of pacemakers influence wave propagation.

Abstract

In an oscillatory medium, a region which oscillates faster than its surroundings can act as a source of outgoing waves. Such pacemaker-generated waves can synchronize the whole medium and are present in many chemical and biological systems, where they are a means of transmitting information at a fixed speed over large distances. In this paper, we apply analytical tools to investigate the factors that determine the speed of these waves. More precisely, we apply singular perturbation and phase reduction methods to two types of negative-feedback oscillators, one built on underlying bistability and one including a time delay in the negative feedback. In both systems, we investigate the influence of timescale separation on the resulting wave speed, as well as the effect of size and frequency of the pacemaker region. We compare our analytical estimates to numerical simulations which we described previously [1].