A Null-model Exhibiting Synchronized Dynamics in Uncoupled Oscillators

Abstract

The phenomenon of phase synchronization of oscillatory systems arising out of feedback coupling is ubiquitous across physics and biology. In noisy, complex systems, one generally observes transient epochs of synchronization followed by non-synchronous dynamics. How does one guarantee that the observed transient epochs of synchronization are arising from an underlying feedback mechanism and not from some peculiar statistical properties of the system? This question is particularly important for complex biological systems where the search for a non-existent feedback mechanism may turn out be an enormous waste of resources. In this article, we propose a null model for synchronization motivated by expectations on the dynamical behaviour of biological systems to provide a quantitative measure of the confidence with which one can infer the existence of a feedback mechanism based on observation of transient synchronized behaviour. We demonstrate the application of our null model to the phenomenon of gait synchronization in free-swimming nematodes, C. elegans.