title: Dynamical quorum-sensing in oscillators coupled through an external medium.
abstract: Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed "dynamical quorum sensing". Synchronization frequently arises through chemical communication via signaling molecules distributed through an external medium. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common medium. We show that this model exhibits a rich phase diagram with four qualitatively distinct physical mechanisms that can lead to a loss of coherent population-level oscillations, including a novel mechanism arising from effective time-delays introduced by the external medium. We derive a single pair of analytic equations that allow us to calculate phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments on BZ catalytic particles as well as synthetically engineered bacteria.
authors.affiliation: Dept. of Molecular Biology and Lewis-Sigler Institute, Princeton University, Princeton, NJ 08854.
authors.forename: David J
authors.initials: DJ
authors.lastname: Schwab
authors.forename: Ania
authors.initials: A
authors.lastname: Baetica
authors.forename: Pankaj
authors.initials: P
authors.lastname: Mehta