ABSTRACT Mutual synchronization is a ubiquitous phenomenon that exists in various natural systems. The individual participants in this process can be modeled as oscillators, which interact by discrete pulses. In this paper, we analyze the synchronization condition of two- and multi-oscillators system, and propose a linear pulse-coupled oscillators model. We prove that the proposed model can achieve synchronization for almost all conditions. Numerical simulations are also included to investigate how different model parameters affect the synchronization. We also discuss the implementation of the model as a new approach for time synchronization in wireless sensor networks.
Cite this paper
nullZ. An, H. Zhu, M. Zhang, C. Xu, Y. Xu and X. Li, "Linear Pulse-Coupled Oscillators Model¬—A New Approach for Time Synchronization in Wireless Sensor Networks," Wireless Sensor Network, Vol. 2 No. 2, 2010, pp. 108-114. doi: 10.4236/wsn.2010.22015.
 K. G. Blair, “Luminous Insects,” Nature, Vol. 96, No. 2406, pp. 411–415, 1915.
C. A. Richmond, “Fireflies flashing in unison,” Science, Vol. 71, No. 1847, pp. 537–538, 1930.
C. S. Peskin, “Self-synchronization of the cardiac pacemaker,” in Mathematical Aspects of Heart Physiology, New York University: New York. pp. 268–278, 1975.
R. E. Mirollo and S. H. Strogatz, “Synchronization of pulse-coupled biological oscillators,” SIAM Journal on Applied Mathematics, Vol. 50, No. 6, pp. 1645–1662, 1990.
Y. Kuramoto, “Self-entrainment of a population of coupled non-linear oscillators,” in International Symposium on Mathematical Problems in Theoretical Physics, pp. 420–422, 1975.
Y. Kuramoto, “Chemical oscillations, waves, and turbulence,” Springer Series in Synergetics, Berlin, Springer-Verlag, pp. 164, 1984.
S. H. Strogatz, “From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators,” Physica D: Nonlinear Phenomena, Vol. 143, No.1–4, pp. 1–20, 2000.
U. Ernst, K. Pawelzik, and T. Geisel, “Synchronization induced by temporal delays in pulse-coupled oscillators,” Physical Review Letters, Vol. 74, No. 9, pp. 1570–1573, 1995.
U. Ernst, K. Pawelzik, and T. Geisel, “Delay-induced multistable synchronization of biological oscillators,” Physical Review E, Vol. 57, No. 2, pp. 2150–2162, 1998.
O. Simeone, et al. “Distributed synchronization in wireless networks.” IEEE Signal Processing Magazine, Vol. 25, No. 5, pp. 81–97, 2008.
Y. W. Hong and A. Scaglione, “Time synchronization and reach-back communications with pulse-coupled oscillators for UWB wireless ad hoc networks,” in Proceedings of IEEE Conference on Ultra Wideband Systems and Technologies, 2003.
Y. W. Hong, and A. Scaglione, “A scalable synchronization protocol for large scale sensor networks and its applications,” IEEE Journal on Selected Areas in Communications, Vol. 23, No. 5, pp. 1085–1099, 2005.
G. Werner-Allen, et al. “Firefly-inspired sensor network synchronicity with realistic radio effects,” in Proceedings of the 3rd international conference on Embedded networked sensor systems. ACM: San Diego, California, USA. pp. 142–153, 2005.