Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators
Statistical Mechanics
2009-10-30 v1 adap-org
Soft Condensed Matter
Adaptation and Self-Organizing Systems
Biological Physics
Abstract
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.
Keywords
Cite
@article{arxiv.cond-mat/9712200,
title = {Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators},
author = {Albert Diaz-Guilera and Conrad J. Perez and Alex Arenas},
journal= {arXiv preprint arXiv:cond-mat/9712200},
year = {2009}
}
Comments
8 pages, 2 ps figures, epsf.sty, RevTeX. To appear in Phys. Rev. E