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arXiv · 0812.0460

Synchronization of extended systems from internal coherence

Gregory S. Duane
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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.

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Gregory S. Duane. 2008-12-02. Synchronization of extended systems from internal coherence. https://doi.org/10.1103/physreve.80.015202

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