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

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.

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

References in corpus (3)

• On Self-Organized Criticality and Synchronization in Lattice Models of Coupled Dynamical Systems
• On Synchronization in a Lattice Model of Pulse-Coupled Oscillators
• Stability of Spatio-Temporal Structures in a Lattice Model of Pulse-Coupled Oscillators

Cited by in corpus (4)

• Synchronization, Diversity, and Topology of Networks of Integrate and Fire Oscillators
• Frequency adjustment and synchrony in networks of delayed pulse coupled oscillators
• Pattern selection in a lattice of pulse-coupled oscillators
• A probability based approach on ananlyzing dynamics of oscillators on a bidirectional ring with propagation delay