TY - JOUR
T1 - Synchronization of pulse-coupled oscillators and clocks under minimal connectivity assumptions
AU - Proskurnikov, Anton V.
AU - Cao, Ming
N1 - Accepted Author Manuscript
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Complex networks
KW - event-triggered control
KW - hybrid systems
KW - pulse-coupled oscillators
KW - synchronization
UR - http://www.scopus.com/inward/record.url?scp=85036460570&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:c8d86423-08a5-4adb-a757-6e9b52251b11
U2 - 10.1109/TAC.2016.2644538
DO - 10.1109/TAC.2016.2644538
M3 - Article
AN - SCOPUS:85036460570
SN - 0018-9286
VL - 62
SP - 5873
EP - 5879
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 11
ER -