Transmission of stimulus-locked responses in two coupled phase oscillators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 5 2, 2004, Pages

  Tass, Peter A ^a,b  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b UNIVERSITY HOSPITAL OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROENCEPHALOGRAPHY; GAUSSIAN NOISE (ELECTRONIC); MAGNETOENCEPHALOGRAPHY; MATHEMATICAL MODELS; MEDICINE; OSCILLATIONS; PHASE LOCKED LOOPS; STOCHASTIC PROGRAMMING; SYNCHRONIZATION;

CROSS-TRIAL (CT) RESPONSE; LOCAL FIELD POTENTIALS (LFP); RANDOM FORCES; STANDARD DEVIATIONS;

OSCILLATORS (ELECTRONIC);

EID: 42749105178     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (64)

1. H. Haken, Advanced Synergetics (Springer, Berlin, 1983).
2. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
3. A. T. Winfree, The Geometry of Biological Time (Springer, Berlin, 1980).
4. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 88, 138103 (2002); B. Naundorf and J. A. Freund, Phys. Rev. E 66, 040901(R) (2002); B. Lindner et al., ibid. 66, 031916 (2002); S. Bahar et al., ibid. 65, 050901 (2002); C. R. Laing and A. Longtin, ibid. 67, 051928 (2003).
5. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 88, 138103 (2002); B. Naundorf and J. A. Freund, Phys. Rev. E 66, 040901(R) (2002); B. Lindner et al., ibid. 66, 031916 (2002); S. Bahar et al., ibid. 65, 050901 (2002); C. R. Laing and A. Longtin, ibid. 67, 051928 (2003).
6. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 88, 138103 (2002); B. Naundorf and J. A. Freund, Phys. Rev. E 66, 040901(R) (2002); B. Lindner et al., ibid. 66, 031916 (2002); S. Bahar et al., ibid. 65, 050901 (2002); C. R. Laing and A. Longtin, ibid. 67, 051928 (2003).
7. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 88, 138103 (2002); B. Naundorf and J. A. Freund, Phys. Rev. E 66, 040901(R) (2002); B. Lindner et al., ibid. 66, 031916 (2002); S. Bahar et al., ibid. 65, 050901 (2002); C. R. Laing and A. Longtin, ibid. 67, 051928 (2003).
8. A. B. Neiman and D. F. Russell, Phys. Rev. Lett. 88, 138103 (2002); B. Naundorf and J. A. Freund, Phys. Rev. E 66, 040901(R) (2002); B. Lindner et al., ibid. 66, 031916 (2002); S. Bahar et al., ibid. 65, 050901 (2002); C. R. Laing and A. Longtin, ibid. 67, 051928 (2003).
9. P. A. Tass, Phase Resetting in Medicine and Biology. Stochastic Modelling and Data Analysis (Springer, Berlin, 1999).
10. H. Steriade et al., Thalamic Oscillations and Signaling (Wiley, New York, 1990).
11. K. H. Chiappa, Evoked Potentials in Clinical Medicine (Raven Press, New York, 1983).
12. B. Sayers et al., Nature (London) 247, 481 (1974).
13. S. Makeig et al., Science 295, 690 (2002).
14. G. D. Dawson, Electroencephalogr. Clin. Neurophysiol. 6, 153 (1954).
15. M. Hämäläinen et al., Rev. Mod. Phys. 65, 413 (1993).
16. A. Frank et al., Physica D 144, 62 (2000).
17. J. A. S. Kelso et al., Phys. Lett. A 169, 134 (1992).
18. A. Daffertshofer et al., Phys. Lett. A 266, 290 (2000).
19. A. Fuchs et al., Phys. Lett. A 266, 303 (2000).
20. H. J. Heinze and H. Kunkel, Methods Inf. Med. 23, 29 (1984).
21. D. O. Walter, Electroencephalogr Clin. Neurophysiol. Suppl. 27, 61 (1969).
22. D. J. Doyle, Electroencephalogr. Clin. Neurophysiol. 38, 533 (1975).
23. J. P. De Weerd, Biol. Cybern. 41, 211 (1981).
24. J. P. De Weerd and J. I. Kap, Biol. Cybern. 41, 223 (1981).
25. R. R. Coifman and M. Y. Wickerhauser, Electroencephalogr Clin. Neurophysiol. Suppl. 45, 57 (1996).
26. S. J. Schiff et al., Electroencephalogr. Clin. Neurophysiol. 91, 442 (1994).
27. S. J. Schiff et al., Opt. Eng. 33, 2162 (1994).
28. V. J. Samar et al., Brain Cogn 27, 398 (1995).
29. A. Effern et al., Physica D 140, 257 (2000).
30. R. Hari and R. Salmelin, Trends Neurosci. 20, 44 (1997).
31. Handbook of Biological Physics, edited by C. Gielen and F. Moss (Elsevier, Amsterdam, 2001), Vol, IV.
32. P. A. Tass, Europhys. Lett. 59, 199 (2002).
33. P. A. Tass, Chaos 13, 364 (2003).
34. P. A. Tass, Phys. Rev. E 67, 051902 (2003).
35. P. A. Tass et al. (unpublished).
36. C. W. Gardiner, Handbook for Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd ed. (Springer, Berlin, 1985).
37. E. Batschelet, Circular Statistics in Biology (Academic Press, London, 1981).
38. E. Batschelet, Statistical Methods for the Analysis of Problems in Animal Orientation and Certain Biological Rhythms (Amer. Inst. Biol. Sci., Washington, D.C., 1965).
39. R. K. Otnes and L. Enochson, Digital Time Series Analysis (Wiley, New York, 1972).
40. J. L. Hodges, Jr., Ann. Math. Stat. 26, 523 (1955).
41. B. Ajne, Biometrika 55, 343 (1968).
42. G. K. Bhattacharyya and R. A. Johnson, Biometrika 56, 446 (1969).
43. J. S. Rao, Indian J. Stat., Ser. B 38, 329 (1976).
44. N. F. Laubscher and G. J. Rudolph, Ann. Math. Stat. 38, 964 (1967).
45. J. S. Rao, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 22, 33 (1972).
46. G. S. Watson, Biometrika 48, 109 (1961).
47. N. H. Kuiper, Proc. K. Ned. Akad. Wet., Ser. A: Math. Sci. 63, 38 (1960).
48. M. A. Stephens, Biometrika 52, 309 (1965).
49. I. G. Abrahamson, Ann. Math. Stat. 38, 1475 (1967).
50. U. R. Maag, Ann. Stat. 1, 1185 (1973).
51. K. Bucher and P. Bättig, Helv. Physiol. Pharmacol. Acta 18, 25 (1960).
52. P. Engel et al., Pfluegers Arch. Gesamte Physiol. Menschen Tiere 298, 258 (1967).
53. M. Schiek, Ph.D. thesis, University of Aachen, 1998 (unpublished).
54. W. J. P. Barnes, J. Comput. Phys. 96, 237 (1975).
55. W. H. Press et al., Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992).
56. H. Forssberg et al., Brain Res. 85, 103 (1975).
57. P. A. Tass et al., Phys. Rev. Lett. 81, 3291 (1998).
58. P. A. Tass et al., Phys. Rev. Lett. 90, 088101 (2003).
59. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963).
60. M. G. Rosenblum et al. Phys. Rev. Lett. 76, 1804 (1996).
61. K. V. Mardia, Statistics of Directional Data (Academic Press, London, 1972).
62. C. Tallon-Baudry et al. J. Neurosci. 16, 4240 (1996).
63. P. Panter, Modulation, Noise, and Spectral Analysis (McGraw-Hill, New York, 1965).
64. R. Quian Quiroga et al., Phys. Rev. E 65, 041903 (2002).