Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

Details Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

1997-12-17

arxiv.org/abs/cond-mat/9712200v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2 ps figures, epsf.sty, RevTeX. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.57.3820

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.

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