Synchronization of extended systems from internal coherence
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.
Keywords
Cite
@article{arxiv.0812.0460,
title = {Synchronization of extended systems from internal coherence},
author = {Gregory S. Duane},
journal= {arXiv preprint arXiv:0812.0460},
year = {2013}
}
Comments
version accepted for publication in PRE (paragraph beginning at the bottom of pg. 5 has been rewritten to suggest unifying principle for synchronizability, applying to both forced-dissipative and Hamiltonian systems; other minor changes)