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The phenomenon of phase synchronization of oscillatory systems arising out offeedback coupling is ubiquitous across physics and biology. In noisy, complexsystems, one generally observes transient epochs of synchronization followed bynon-synchronous dynamics. How does one guarantee that the observed transientepochs of synchronization are arising from an underlying feedback mechanism andnot from some peculiar statistical properties of the system? This question isparticularly important for complex biological systems where the search for anon-existent feedback mechanism may turn out be an enormous waste of resources.In this article, we propose a null model for synchronization motivated byexpectations on the dynamical behaviour of biological systems to provide aquantitative measure of the confidence with which one can infer the existenceof a feedback mechanism based on observation of transient synchronizedbehaviour. We demonstrate the application of our null model to the phenomenonof gait synchronization in free-swimming nematodes, C. elegans.

A Null-model Exhibiting Synchronized Dynamics in Uncoupled Oscillators