We study the effect of population variability on the collective dynamics of interacting cyclic active elements, modeled as oscillators whose frequencies are a sum of a deterministic part, identical for all elements, and a random part. The random part can vary both in amplitude and over time yielding quenched or annealed temporal disorder, as well as an intermediate regime where the noise varies over a timescale comparable to the period. In the absence of randomness, the elements synchronize in phase and spontaneous coherent motion emerges. However, if the population variability is large enough, then synchronization is lost. This transition to a nonsynchronized state is governed by properties of the tail of the population distribution that can be understood by an analysis of the properties of a random matrix. We find that collections of elements with annealed temporal disorder can tolerate, remaining functional (i.e., synchronized), higher levels of variability than the quenched cases. This places design constraints on functional synthetic biological systems in the presence of unavoidable disorder.
- Bristol BioDesign Institute
- Synthetic Biology