Synchronous phase clustering in a network of neurons with spatially decaying excitatory coupling

Journal of the Physical Society of Japan

Volumn 72, Issue 2, 2003, Pages 443-447

  Wang, Yuqing ^a,b   Wang, Z D ^a   Li, Y X ^b   Pei, X ^c,d  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^d ST JUDE MEDICAL   (United States)

Author keywords

Network; Neuron; Noise; Synchronization

Indexed keywords

ARTICLE; LEARNING; MOLECULAR DYNAMICS; MOLECULAR INTERACTION; MOLECULAR MODEL; OSCILLATION; PHASE TRANSITION; SYNAPSE;

EID: 0037241311     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.72.443     Document Type: Article

References (36)

1. C. M. Gray et al: Nature (London) 338 (1989) 334; P. Roelfsma et al.: J. Cog. Neurosci. 8 (1996) 603; F. P. Roelfsma et al.: Proc. Natl. Acad. Sci. USA 94 (1997) 12699; M. A. L. Nicolelis et al.: Science 268 (1995) 1353; A. Riehle et al.: ibid. 278 (1997) 1950.
2. C. M. Gray et al: Nature (London) 338 (1989) 334; P. Roelfsma et al.: J. Cog. Neurosci. 8 (1996) 603; F. P. Roelfsma et al.: Proc. Natl. Acad. Sci. USA 94 (1997) 12699; M. A. L. Nicolelis et al.: Science 268 (1995) 1353; A. Riehle et al.: ibid. 278 (1997) 1950.
3. C. M. Gray et al: Nature (London) 338 (1989) 334; P. Roelfsma et al.: J. Cog. Neurosci. 8 (1996) 603; F. P. Roelfsma et al.: Proc. Natl. Acad. Sci. USA 94 (1997) 12699; M. A. L. Nicolelis et al.: Science 268 (1995) 1353; A. Riehle et al.: ibid. 278 (1997) 1950.
4. C. M. Gray et al: Nature (London) 338 (1989) 334; P. Roelfsma et al.: J. Cog. Neurosci. 8 (1996) 603; F. P. Roelfsma et al.: Proc. Natl. Acad. Sci. USA 94 (1997) 12699; M. A. L. Nicolelis et al.: Science 268 (1995) 1353; A. Riehle et al.: ibid. 278 (1997) 1950.
5. C. M. Gray et al: Nature (London) 338 (1989) 334; P. Roelfsma et al.: J. Cog. Neurosci. 8 (1996) 603; F. P. Roelfsma et al.: Proc. Natl. Acad. Sci. USA 94 (1997) 12699; M. A. L. Nicolelis et al.: Science 268 (1995) 1353; A. Riehle et al.: ibid. 278 (1997) 1950.
6. R. E. Mirollo and S. H. Strogatz: SIAM J. Appl. Math. 50 (1990) 1645; D. Hansel and H. Sompolinsky: Phys. Rev. Lett. 68 (1992) 718; P. C. Bressloff and S. Coombes: ibid. 78 (1997) 4665; W. Wang, G. Chen and Z. D. Wang: Phys. Rev. E 56 (1997) 3728; Y. Wang, D. T. W. Chik and Z. D. Wang: ibid. 61 (2000) 740.
7. R. E. Mirollo and S. H. Strogatz: SIAM J. Appl. Math. 50 (1990) 1645; D. Hansel and H. Sompolinsky: Phys. Rev. Lett. 68 (1992) 718; P. C. Bressloff and S. Coombes: ibid. 78 (1997) 4665; W. Wang, G. Chen and Z. D. Wang: Phys. Rev. E 56 (1997) 3728; Y. Wang, D. T. W. Chik and Z. D. Wang: ibid. 61 (2000) 740.
8. R. E. Mirollo and S. H. Strogatz: SIAM J. Appl. Math. 50 (1990) 1645; D. Hansel and H. Sompolinsky: Phys. Rev. Lett. 68 (1992) 718; P. C. Bressloff and S. Coombes: ibid. 78 (1997) 4665; W. Wang, G. Chen and Z. D. Wang: Phys. Rev. E 56 (1997) 3728; Y. Wang, D. T. W. Chik and Z. D. Wang: ibid. 61 (2000) 740.
9. R. E. Mirollo and S. H. Strogatz: SIAM J. Appl. Math. 50 (1990) 1645; D. Hansel and H. Sompolinsky: Phys. Rev. Lett. 68 (1992) 718; P. C. Bressloff and S. Coombes: ibid. 78 (1997) 4665; W. Wang, G. Chen and Z. D. Wang: Phys. Rev. E 56 (1997) 3728; Y. Wang, D. T. W. Chik and Z. D. Wang: ibid. 61 (2000) 740.
10. R. E. Mirollo and S. H. Strogatz: SIAM J. Appl. Math. 50 (1990) 1645; D. Hansel and H. Sompolinsky: Phys. Rev. Lett. 68 (1992) 718; P. C. Bressloff and S. Coombes: ibid. 78 (1997) 4665; W. Wang, G. Chen and Z. D. Wang: Phys. Rev. E 56 (1997) 3728; Y. Wang, D. T. W. Chik and Z. D. Wang: ibid. 61 (2000) 740.
11. A. K. Engel et al.: Science 252 (1991) 1177.
12. U. Ernst, K. Pawelzik and T. Geisel: Phys. Rev. Lett. 74 (1995) 1570.
13. U. Ernst, K. Pawelzik and T. Geisel: Phys. Rev. E 57 (1998) 2150.
14. D. Hansel, G. Mato and C. Meunier: Neural Comput. 7 (1995) 307; X. J. Wang, D. Colomb and J. Rinzel: Proc. Natl. Acad. Sci. USA 92 (1995) 5577; J. A. White et al.: J. Comput. Neurosci. S (1997) 5.
15. D. Hansel, G. Mato and C. Meunier: Neural Comput. 7 (1995) 307; X. J. Wang, D. Colomb and J. Rinzel: Proc. Natl. Acad. Sci. USA 92 (1995) 5577; J. A. White et al.: J. Comput. Neurosci. S (1997) 5.
16. D. Hansel, G. Mato and C. Meunier: Neural Comput. 7 (1995) 307; X. J. Wang, D. Colomb and J. Rinzel: Proc. Natl. Acad. Sci. USA 92 (1995) 5577; J. A. White et al.: J. Comput. Neurosci. S (1997) 5.
17. L. Neltner, D. Hansel, G. Mato and C. Meunier: Neural Comput. 12 (2000) 1607; N. Brunel: J. Comput. Neurosci. 8 (2000) 183; N. Brunel and V. Hakim: Neural Comput. 11 (1999) 1621.
18. L. Neltner, D. Hansel, G. Mato and C. Meunier: Neural Comput. 12 (2000) 1607; N. Brunel: J. Comput. Neurosci. 8 (2000) 183; N. Brunel and V. Hakim: Neural Comput. 11 (1999) 1621.
19. L. Neltner, D. Hansel, G. Mato and C. Meunier: Neural Comput. 12 (2000) 1607; N. Brunel: J. Comput. Neurosci. 8 (2000) 183; N. Brunel and V. Hakim: Neural Comput. 11 (1999) 1621.
20. The state was also observed in some globally coupled nonlinear oscillators. See, e.g., D. Golomb et al: Phys. Rev. A 45 (1992) 3516; C. van Vreeswijk and L. F. Abbott: SIAM J. Appl. Math. 53 (1993) 253.
21. The state was also observed in some globally coupled nonlinear oscillators. See, e.g., D. Golomb et al: Phys. Rev. A 45 (1992) 3516; C. van Vreeswijk and L. F. Abbott: SIAM J. Appl. Math. 53 (1993) 253.
22. 2 was also tried. The conclusion regarding synchronous phase clustering is essentially the same as that for 1/R.
23. H. A. Braun et al: Int. J. Bifurcation Chaos 8 (1998) 881; A. Neiman et al: Phys. Rev. Lett. 82 (1999) 660.
24. H. A. Braun et al: Int. J. Bifurcation Chaos 8 (1998) 881; A. Neiman et al: Phys. Rev. Lett. 82 (1999) 660.
25. R. Gilmore, X. Pei and F. Moss: Chaos 9 (1999) 812.
26. In this paper, the parameters in the equation are the same as those in refs. 10 and 11, which were determined from experimental data on peripheral cold receptors.
27. J. J. B. Jack, D. Noble and R. W. Tsien: Electric Current Flow in Excitable Cells (Clarendon Press, Oxford, 1983); W. Gestner and J. L. van Hemmen: Models of Neural Networks II, ed. E. Domany, J. L. van Hemmen and K. Schulten, (Springer-Verlag, Heidelberg, 1994) pp. 1-85.
28. J. J. B. Jack, D. Noble and R. W. Tsien: Electric Current Flow in Excitable Cells (Clarendon Press, Oxford, 1983); W. Gestner and J. L. van Hemmen: Models of Neural Networks II, ed. E. Domany, J. L. van Hemmen and K. Schulten, (Springer-Verlag, Heidelberg, 1994) pp. 1-85.
29. syn〉, the average value of the coupling term).
30. If we employ uniform inhibitory or excitatory coupling, the main results are the same as those in refs. 4 and 5, where an integrate-and fire model and a HH model are employed.
31. Y. Kuramoto: Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Tokyo, 1984).
32. L. Ren and G. B. Ermentrout: SIAM J. Math. Anal. 29 (1998) 208; C. van Vreeswijk, L. F. Abbott and G. B. Ermentrout: Neural Comput. 1 (1994) 313.
33. L. Ren and G. B. Ermentrout: SIAM J. Math. Anal. 29 (1998) 208; C. van Vreeswijk, L. F. Abbott and G. B. Ermentrout: Neural Comput. 1 (1994) 313.
34. The Adjoint of the modified HH model is calculated by using the software XPPAUT, developed by G. B. Ermentrout.
35. G. Buzsaki et al: Science 256 (1992) 1025; J. J. Chrobak and G. Buzsaki: J. Neurosci. 16 (1996) 3056.
36. G. Buzsaki et al: Science 256 (1992) 1025; J. J. Chrobak and G. Buzsaki: J. Neurosci. 16 (1996) 3056.