Synchronization of Pulse-Coupled Oscillators and Clocks Under Minimal Connectivity Assumptions

Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used in wireless sensor networks, providing clock synchronization...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 62; no. 11; pp. 5873 - 5879
Main Authors Proskurnikov, Anton V., Ming Cao
Format Journal Article
LanguageEnglish
Published IEEE 01.11.2017
Subjects
Clocks
Complex networks
Control systems
Couplings
event-triggered control
hybrid systems
Mathematical model
Nickel
Oscillators
pulse-coupled oscillators
Synchronization
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Summary:Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used in wireless sensor networks, providing clock synchronization with parsimonious packet exchanges. In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and general phase-response curves of the oscillators. The most general results of this type (Wang et al., 2012, 2015) establish synchronization of oscillators with a delay-advance phase-response curve over strongly connected networks. In this technical note we extend this result by relaxing the connectivity condition to the existence of a root node (or a directed spanning tree) in the graph. This condition is also necessary for synchronization.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2644538