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 Belousov–Zhabotinsky catalytic particles as well as synthetically engineered bacteria.

许多生物和物理系统在一个通常被称为“动态群体感应”的过程中表现出人口密度依赖性向同步振荡的转变。同步经常通过通过外部介质分布的信号分子的化学通讯产生。我们研究了一个简单的动态群体感应理论模型：通过共同介质扩散耦合的极限循环振荡器的异质群体。我们表明，该模型展示了一个丰富的相图，其中包含四种性质不同的物理机制，可导致相干种群水平振荡的损失，包括由外部介质引入的有效时间延迟引起的新机制。