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Numerous biological systems exhibit transitions to synchronised oscillationsvia a population-density-dependant mechanism known as quorum sensing. Here wepropose a model system, based on spatially distributed limit-cycle oscillators,that allows us to capture the dynamics of synchronization fronts by taking thecontinuum limit as the number of coupled oscillators tends to infinity. Weexplore analytically a family of wavefront-type solutions to the system interms of model parameters and corroborate its validity via a numericalfinite-difference method algorithm. Finally, we review our results in light ofsome experimental systems in synthetic biology based on a synchronised quorumof genetic clocks, coupled via a diffusive auto-inducer signalling moleculeanalogue to our Hooke-like coupling scheme within the proposed hybridRayleigh-van der Pol model.

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