Synchronization Fronts in a Spatially Extended System of Hybrid Rayleigh-van der Pol Oscillators

TL;DR

This paper models synchronization fronts in spatially extended hybrid Rayleigh-van der Pol oscillators, capturing quorum sensing-like dynamics and analyzing wavefront solutions both analytically and numerically, with relevance to synthetic biology.

Contribution

It introduces a continuum model of coupled oscillators that describes synchronization fronts, linking theoretical analysis with experimental biological systems.

Findings

Analytical wavefront solutions derived for the model

Numerical validation confirms the analytical results

Relevance demonstrated for synthetic biology quorum sensing systems

Abstract

Numerous biological systems exhibit transitions to synchronised oscillations via a population-density-dependant mechanism known as quorum sensing. Here we propose a model system, based on spatially distributed limit-cycle oscillators, that allows us to capture the dynamics of synchronization fronts by taking the continuum limit as the number of coupled oscillators tends to infinity. We explore analytically a family of wavefront-type solutions to the system in terms of model parameters and corroborate its validity via a numerical finite-difference method algorithm. Finally, we review our results in light of some experimental systems in synthetic biology based on a synchronised quorum of genetic clocks, coupled via a diffusive auto-inducer signalling molecule analogue to our Hooke-like coupling scheme within the proposed hybrid Rayleigh-van der Pol model.