Stochastic phase dynamics and noise-induced mixed-mode oscillations in coupled oscillators

Chaos

Volumn 18, Issue 1, 2008, Pages

  Yu, Na ^a   Kuske, Rachel ^a   Li, Yue Xian ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41549090427     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2790369     Document Type: Article

References (46)

1. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, New York, 1984).
2. G. B. Ermentrout and N. Kopell, SIAM J. Math. Anal. 15, 215 (1984).
3. C. Van Vreeswijk, L. F. Abbott, and G. B. Ermentrout, J. Comput. Neurosci. 1, 313 (1994).
4. D. Hansel, G. Mato, and C. Meunier, Neural Comput. 7, 307 (1995).
5. Z. F. Mainen and T. J. Sejnowski, Science 268, 1503 (1995).
6. D. A. McCormick, Science 285, 541 (1999).
7. X. Pei and L. Wilkens, and F. Moss, Phys. Rev. Lett. 77, 4679 (1996).
8. A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. 78, 775 (1997).
9. S. G. Lee, A. Neiman, and S. Kim, Phys. Rev. E 57, 3292 (1998).
10. A. Neiman, L. Schimansky-Geier, A. Cornell-Bell, and F. Moss, Phys. Rev. Lett. 83, 4896 (1999).
11. T. Mori and S. Kai, Phys. Rev. Lett. 88, 218101 (2002).
12. S. Bahar, A. Neiman, L. A. Wilkens, and F. Moss, Phys. Rev. Lett. 69, 050901 (2002).
13. S. Bahar and F. Moss, Chaos 13, 138 (2003).
14. D. Paydarfar, D. B. Forger, and J. R. Clay, J. Neurophysiol. 96, 3338 (2006).
15. C. Morris and H. Lecar, Biophys. J. 35, 193 (1981).
16. M. Koper, Physica D 80, 72 (1995).
17. H. G. Rotstein and R. Kuske, Physica D 215, 46 (2006).
18. A. F. Vakakis and C. Cetinkaya, SIAM J. Appl. Math. 53, 265 (1993).
19. R. Kuske and T. Erneux, Eur. J. Appl. Math. 8, 389 (1997).
20. R. Kuske and T. Erneux, Opt. Commun. 139, 125 (1997).
21. H. G. Rotstein, N. Kopell, A. Zhabotinsky, and I. R. Epstein, J. Chem. Phys. 119, 8824 (2003).
22. H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, and I. R. Epstein, SIAM J. Appl. Math. 63, 1098 (2003).
23. L. Yang and I. R. Epstein, Phys. Rev. E 69, 026211 (2004).
24. R. H. Rand and P. J. Holmes, Int. J. Nonlinear Mechanics 15, 387 (1980).
25. G. B. Ermentrout, J. Math. Biol. 12, 327 (1981).
26. D. G. Aronson, G. B. Ermentrout, and N. Kopell, Physica D 41, 403 (1990).
27. A. Sherman and J. Rinzel, Proc. Natl. Acad. Sci. U.S.A. 89, 2471 (1992).
28. A. Sherman, Bull. Math. Biol. 56, 811 (1994).
29. S. H. Park, S. Kim, H. B. Pyo, and S. Lee, Phys. Rev. E 60, 2177 (1999).
30. D. Hansel, G. Mato, and C. Meunier, Europhys. Lett. 23, 367 (1993).
31. G. S. Cymbalyuk, E. V. Nikolaev, and R. M. Borisyuk, J. Biol. Cybern 71, 153 (1994).
32. N. Kopell and D. Somers, J. Math. Biol. 33, 261 (1995).
33. G. De Vries, A. Sherman, and H. S. Zhu, Bull. Math. Biol. 60, 1167 (1998).
34. M. Bindschadler and J. Sneyd, Chaos 11, 237 (2001).
35. D. Hansel and G. Mato, Physica A 200, 662 (1993).
36. Z. Zheng, G. Hu, and B. Hu, Phys. Rev. Lett. 81, 5318 (1998).
37. Y. Wang, D. T. W. Chik, and Z. D. Wang, Phys. Rev. E 61, 740 (2000).
38. B. Lindner, J. Garcia-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. 392, 321 (2004).
39. J. M. Casado and J. P. Baltanas, Phys. Rev. E 68, 061917 (2003).
40. B. Hu and C. Zhou, Phys. Rev. E 61, R1001 (2000).
41. H. Hong and M. Y. Choi, Phys. Rev. E 62, 6462 (2000).
42. M. Ohtaki, T. Tanaka, and K. Miyakawa, Phys. Rev. E 70, 056219 (2004).
43. C. Zhou and J. Kurths, Phys. Rev. E 65, 040101 (2002).
44. E. J. Doedel, R. C. Paffenroth, A. R. Champneys, T. F. Fairgrieve, Yu. A. Kuznetsov, B. Sandstede, and X. Wang, Technical Report, Caltech, February, 2001.
45. http://www.math.pitt.edu/~bard/xpp/xpp.html.
46. M. H. Holms, Introduction to Perturbation Methods (Springer-Verlag, New York, 1995).