Synchronization of Pulse-Coupled Oscillators on (Strongly) Connected Graphs

The synchronization of pulse-coupled oscillators (PCOs) interacting on general (strongly) connected graphs is addressed. It is shown that the network synchronizes if the phases are contained in an arc of length less than π, for every (strongly) connected interaction topology. Moreover, global synchronization is feasible in the all-to-all, strongly rooted, and connected bidirectional cases. Examples, counter-examples, and numerical simulations are given to illustrate the analytical findings.

[1]  Yongqiang Wang,et al.  Optimal Phase Response Functions for Fast Pulse-Coupled Synchronization in Wireless Sensor Networks , 2012, IEEE Transactions on Signal Processing.

[2]  J. Buck.  Synchronous Rhythmic Flashing of Fireflies , 1938, The Quarterly Review of Biology.

[3]  A. Mauroy.  On the dichotomic collective behaviors of large populations of pulse-coupled firing oscillators , 2011 .

[4]  Florian Dörfler,et al.  On the Critical Coupling for Kuramoto Oscillators , 2010, SIAM J. Appl. Dyn. Syst..

[5]  Yongqiang Wang,et al.  Bio-inspired Synchronization of Non-Identical Pulse-Coupled Oscillators Subject to a Global Cue and Local Interactions , 2012, ADHS.

[6]  Rodolphe Sepulchre,et al.  Kick synchronization versus diffusive synchronization , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  Joel Nishimura,et al.  Robust convergence in pulse-coupled oscillators with delays. , 2011, Physical review letters.

[8]  Yongqiang Wang,et al.  Global synchronization of pulse-coupled oscillators interacting on cycle graphs , 2014, Autom..

[9]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[10]  Yongqiang Wang,et al.  Bio-inspired synchronization of wireless sensor networks for acoustic event detection systems , 2012, 2012 IEEE International Symposium on Precision Clock Synchronization for Measurement, Control and Communication Proceedings.

[11]  J. Buck.  Synchronous Rhythmic Flashing of Fireflies. II. , 1938, The Quarterly Review of Biology.

[12]  Yongqiang Wang,et al.  Energy-Efficient Pulse-Coupled Synchronization Strategy Design for Wireless Sensor Networks Through Reduced Idle Listening , 2012, IEEE Transactions on Signal Processing.

[13]  Charles S. Peskin,et al.  Mathematical aspects of heart physiology , 1975 .

[14]  Srisairam Achuthan,et al.  Pulse coupled oscillators and the phase resetting curve. , 2010, Mathematical biosciences.

[15]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[16]  Roberto Pagliari,et al.  Scalable Network Synchronization with Pulse-Coupled Oscillators , 2011, IEEE Transactions on Mobile Computing.

[17]  Yongqiang Wang,et al.  Bio-inspired hybrid control of pulse-coupled oscillators and application to synchronization of a wireless network , 2012, 2012 American Control Conference (ACC).

[18]  Francis J. Doyle,et al.  Increasing sync rate of , 2012 .

[19]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..