Phase reduction method for strongly perturbed limit cycle oscillators

Physical Review Letters

Volumn 111, Issue 21, 2013, Pages

  Kurebayashi, Wataru ^a   Shirasaka, Sho ^a   Nakao, Hiroya ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CONVENTIONAL METHODS; LIMIT-CYCLE OSCILLATORS; OSCILLATOR DYNAMICS; PHASE REDUCTION METHODS; SYNCHRONIZATION DYNAMICS; SYNCHRONIZATION PROPERTY; THEORETICAL INVESTIGATIONS; WEAK PERTURBATION;

ATOMIC PHYSICS; PHYSICS;

OSCILLISTORS;

EID: 84888313200     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.111.214101     Document Type: Article

References (35)

1. A. T. Winfree, The Geometry of Biological Time (Springer, New York, 2001).
2. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Dover, New York, 2003).
3. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, England, 2001).
4. F. C. Hoppensteadt and E. M. Izhikevich, Weakly Connected Neural Networks (Springer, New York, 1997).
5. G. B. Ermentrout and D. H. Terman, Mathematical Foundations of Neuroscience (Springer, New York, 2010).
6. E. Brown, J. Moehlis, and P. Holmes, Neural Comput. 16, 673 (2004). NEUCEB 0899-7667 10.1162/089976604322860668
7. K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. 65, 1749 (1990); PRLTAO 0031-9007 10.1103/PhysRevLett.65.1749
8. S. H. Strogatz, D. M. Abrams, A. McRobie, B. Eckhardt, and E. Ott, Nature (London) 438, 43 (2005); NATUAS 0028-0836 10.1038/438043a
9. I. Z. Kiss, C. G. Rusin, H. Kori, and J. L. Hudson, Science 316, 1886 (2007). SCIEAS 0036-8075 10.1126/science.1140858
10. J. Garcia-Ojalvo, M. B. Elowitz, and S. H. Strogatz, Proc. Natl. Acad. Sci. U.S.A. 101, 10955 (2004); PNASA6 0027-8424 10.1073/pnas.0307095101
11. S. De Monte, F. d'Ovidio, S. Danø, and P. G. Sørensen, Proc. Natl. Acad. Sci. U.S.A. 104, 18377 (2007); PNASA6 0027-8424 10.1073/pnas.0706089104
12. A. F. Taylor, M. R. Tinsley, F. Wang, Z. Huang, and K. Showalter, Science 323, 614 (2009); SCIEAS 0036-8075 10.1126/science.1166253
13. T. Danino, O. Mondragón-Palomino, L. Tsimring, and J. Hasty, Nature (London) 463, 326 (2010). NATUAS 0028-0836 10.1038/nature08753
14. D. G. Aronson, G. B. Ermentrout, and N. Kopell, Physica (Amsterdam) 41D, 403 (1990); PDNPDT 0167-2789 10.1016/0167-2789(90)90007-C
15. R. E. Mirollo and S. H. Strogatz, J. Stat. Phys. 60, 245 (1990); JSTPBS 0022-4715 10.1007/BF01013676
16. D. Hansel, G. Mato, and C. Meunier, Neural Comput. 7, 307 (1995); NEUCEB 0899-7667 10.1162/neco.1995.7.2.307
17. I. Z. Kiss, W. Wang, and J. L. Hudson, J. Phys. Chem. B 103, 11433 (1999); JPCBFK 1520-6106 10.1021/jp992471h
18. P. C. Bressloff and S. Coombes, Neural Comput. 12, 91 (2000); NEUCEB 0899-7667 10.1162/089976600300015907
19. Y. Zhai, I. Z. Kiss, and J. L. Hudson, Phys. Rev. E 69, 026208 (2004). PLEEE8 1539-3755 10.1103/PhysRevE.69.026208
20. V. Hakim and W. J. Rappel, Phys. Rev. A 46, R7347 (1992); PLRAAN 1050-2947 10.1103/PhysRevA.46.R7347
21. N. Nakagawa and Y. Kuramoto, Prog. Theor. Phys. 89, 313 (1993); PTPKAV 0033-068X 10.1143/ptp/89.2.313
22. H. Nakao and A. S. Mikhailov, Phys. Rev. E 79, 036214 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.79.036214
23. K. Yoshimura and K. Arai, Phys. Rev. Lett. 101, 154101 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.101.154101
24. J.-N. Teramae, H. Nakao, and G. B. Ermentrout, Phys. Rev. Lett. 102, 194102 (2009); PRLTAO 0031-9007 10.1103/PhysRevLett.102.194102
25. D. S. Goldobin, J.-N. Teramae, H. Nakao, and G. B. Ermentrout, Phys. Rev. Lett. 105, 154101 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.154101
26. V. Novičenko and K. Pyragas, Physica (Amsterdam) 241D, 1090 (2012); PDNPDT 0167-2789 10.1016/j.physd.2012.03.001
27. K. Kotani, I. Yamaguchi, Y. Ogawa, Y. Jimbo, H. Nakao, and G. B. Ermentrout, Phys. Rev. Lett. 109, 044101 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.044101
28. Y. Kawamura, H. Nakao, K. Arai, H. Kori, and Y. Kuramoto, Phys. Rev. Lett. 101, 024101 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.101.024101
29. Y. Kawamura, H. Nakao, and Y. Kuramoto, Phys. Rev. E 84, 046211 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.046211
30. E. M. Izhikevich, SIAM J. Appl. Math. 60, 1789 (2000). SMJMAP 0036-1399 10.1137/S0036139999351001
31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.111.214101 for a detailed derivation and discussion.
32. J. P. Keener, Principles of Applied Mathematics: Transformation and Approximation (Addison-Wesley, Boston, 1988).
33. G. B. Ermentrout, J. Math. Biol. 12, 327 (1981). JMBLAJ 0303-6812 10.1007/BF00276920
34. J. A. Sanders and F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems (Springer-Verlag, New York, 1985).
35. T. B. Kepler and M. L. Kagan, Phys. Rev. Lett. 66, 847 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.66.847