Dynamical quorum-sensing and synchronization of nonlinear oscillators coupled through an external medium

Biology – Quantitative Biology – Cell Behavior

Scientific paper

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17 pages including Supporting Information, 3 figures, submitted to Physical Review Letters

Scientific paper

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 media. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common media. We show that this model exhibits a rich phase diagram with four qualitatively distinct mechanisms fueling population-dependent transitions to global oscillations, including a new type of transition we term "dynamic death". We derive a single pair of analytic equations that allows us to calculate all phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments of BZ catalytic particles as well as synthetically engineered bacteria.

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