Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.
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Using tools from the study of aggregation phenomena, exact results are obtained for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.Abstract:
We consider models of identical pulse-coupled oscillators with global interactions Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchronyread more
Citations
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Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Proceedings ArticleDOI
A review of swarmalators and their potential in bio-inspired computing
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The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators.
TL;DR: The introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space and the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-nodebifurcation curves for the limit cycles on the torus.
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Random heterogeneity outperforms design in network synchronization.
TL;DR: In this article, the authors show that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony and that at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization.
Journal ArticleDOI
Convergence Results on Pulse Coupled Oscillator Protocols in Locally Connected Networks
TL;DR: In this paper, the convergence of a locally connected network of pulse coupled oscillator (PCO) to synchronous and desynchronous states, and their implication in terms of the decentralized synchronization and scheduling in communication networks is analyzed.
References
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Journal ArticleDOI
The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Book
The geometry of biological time
TL;DR: The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways is presented.
Journal ArticleDOI
Synchronization of pulse-coupled biological oscillators
TL;DR: A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker is studied in this article, which consists of a population of identical integrate-and-fire oscillators, whose coupling between oscillators is pulsatile: when a given oscillator fires, it pulls the others up by a fixed amount, or brings them to the firing threshold, whichever is less.
BookDOI
Synchronization: Theory and Application
TL;DR: In this article, the basic principles of direct chaotic communications are presented for modeling diversity by chaos and classification by synchronization in high-dimensional dynamical systems, including cycled attractors of coupled cell systems and dynamics with symmetry.