Synchronization of metronomes

American Journal of Physics

Volumn 70, Issue 10, 2002, Pages 992-1000

  Pantaleone, James ^a  

^a UNIVERSITY OF ALASKA ANCHORAGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31644437318     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1501118     Document Type: Article

References (34)

1. R. C. Hilborn and N. B. Tufillaro, "Resource Letter: ND-1: Nonlinear dynamics," Am. J. Phys. 65, 822-834 (1997).
2. H. H. Strogatz and I. Stewart, "Coupled oscillators and biological synchronization," Sci. Am. 269, 102-109 (1993).
3. S. H. Strogatz, "Norbert Wiener's brain waves," Lect. Notes Biomath. 100, 122-138 (1994).
4. See J. Cooley and D. Marshall, "Periodical cicada Page," University of Michigan Museum of Zoology, http://www.ummz.lsa.umich.edu/ magicicada/Periodical/; F. C. Hoppenstedt and J. B. Keller, " Synchronization of periodical cicada emergences," Science 194, 335-337 (1976).
5. D. Attenborough, "The Trials of Life: Talking to Strangers" (BBC-TV, 1991), available from Turner Home Entertainment.
6. D. C. Michaels, E. P. Matyas, and J. Jalife, "Mechanisms of sinoatrial pacemaker synchronization: A new hypothesis," Circ. Res. 61, 704-714 (1987).
7. Z. Neda, E. Ravasz, Y. Brechet, T. Vicsek, and A.-L. Barabasi, "Self-organizing processes: The sound of many hands clapping," Nature (London) 403, 849-850 (2000).
8. K. Wiesenfeld, P. Colet, and S. H. Strogatz, "Synchronization transitions in a disordered Josephson series array," Phys. Rev. Lett. 76, 404-407 (1996).
9. T. Heath and K. Wiesenfeld, "Mutual entrainment of two nonlinear oscillators," Am. J. Phys. 66, 860-866 (1998).
10. V. A. Kostelecky, J. Pantaleone, and S. Samuel, "Neutrino oscillation in the early universe," Phys. Lett. B 315, 46-50 (1993);
11. J. Pantaleone, "Stability of incoherence in an isotropic gas of oscillating neutrinos," Phys. Rev. D 58, 073002-1-073002-14 (1998).
12. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990);
13. A. S. Pikovsky, "On the interaction of strange attractors," Z. Phys. B: Condens. Matter 55, 149-154 (1984);
14. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "Phase synchronization of chaotic oscillators," Phys. Rev. Lett. 76, 1804-1807 (1996).
15. C. Hugenii, Horoloquim Oscilatorium (Apud F. Muguet, Paris, France, 1673);
16. English translation, The Pendulum Clock (Iowa State University Press, Ames, Iowa, 1986).
17. Navigation at sea was extremely difficult for many centuries until reliable clocks were developed in the late 1700s. See, for example, D. Sobel, Longitude (Walker and Co., New York, 1995).
18. B. Bennett, M. F. Schatz, H. Rockwood, and K. Wisenfeld, "Huygens' clocks," Proc. R. Soc. London, Ser. A 458, 563-579 (2002).
19. D. J. Kortweg, "Les Horloges Sympathiques de Huygens" (Archives Neerlandaises, Serie II. Tome XI, Martinus Nijhoff, The Hague, 1906), pp. 273-295.
20. I. I. Blekhman, Synchronization in Science and Technology (ASME, New York, 1988).
21. B. van der Pol, "Forced oscillators in a circuit with non-linear resistance," Philos. Mag. 3, 64-80 (1927).
22. A. T. Winfree, "Biological rhythms and the behavior of populations of coupled oscillators," J. Theor. Biol. 16, 15-42 (1967).
23. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984).
24. The escapement controls the speed and regularity of the pendulum. It transfers the energy stored in the spring to the motion of the pendulum by means of wheels, gears, and ratchets.
25. S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Publishing, Cambridge, 1994).
26. G. R. Fowles, Analytical Mechanics (Holt Rinehart and Winston, New York, 1977).
27. PASCO Scientific, http://www.pasco.com/
28. Y. Kuramoto and J. Nishikawa, "Statistical macrodynamics of large dynamical systems," J. Stat. Phys. 49, 569-605 (1987);
29. S. H. Strogatz and R. E. Mirollo, "Stability of incoherence in a population of coupled oscillators," ibid. 63, 613-635 (1991);
30. L. L. Bonilla, J. C. Neu, and R. Spigler, "Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators," ibid. 67, 313-330 (1992);
31. H. Daido, "Generic scaling at the onset of macroscopic mutual entrainment in limit-cycle oscillators with uniform all-to-all coupling," Phys. Rev. Lett. 73, 760-763 (1994);
32. J. D. Crawford, "Amplitude expansion for instabilities in populations of globally-coupled oscillators," J. Stat. Phys. 74, 1047-1084 (1994).
33. S. H. Strogatz, "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators," Physica D 143, 1-20 (2000).
34. J. Pantaleone (unpublished).