Synchronization of extended systems from internal coherence

TL;DR

This paper explores conditions for synchronizing coupled PDE systems, extending previous results to Hamiltonian systems and demonstrating a weaker synchronization form through scalar field models in an expanding universe.

Contribution

It generalizes the internal coherence condition for synchronization to Hamiltonian systems and illustrates a weaker synchronization form in cosmological scalar fields.

Findings

Internal coherence predicts synchronizability in PDE systems.

Full synchronization is impossible due to Liouville's theorem.

Weak synchronization manifests as positional coincidence of oscillons.

Abstract

A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously illustrated in a forced-dissipative system, and is here extended to Hamiltonian systems, using an example from particle physics. Full synchronization is precluded by Liouville's theorem. A form of synchronization weaker than "measure synchronization" is manifest as the positional coincidence of coherent oscillations ("breathers" or "oscillons") in a pair of coupled scalar field models in an expanding universe with a nonlinear potential, and does not occur with a variant of the model that does not exhibit oscillons.