Generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena

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

Volumn 75, Issue 1, 2007, Pages

  Sato, Yasuomi Daishin ^a,b   Shiino, Masatoshi ^b  

^a FRANKFURT INSTITUTE FOR ADVANCED STUDIES   (Germany)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

IMPULSE RESPONSE; MATHEMATICAL MODELS; NEUROLOGY; RELAXATION PROCESSES;

COUPLING PROPERTIES; RELAXATION RATES; SYNAPTIC COUPLING;

SYNCHRONIZATION;

EID: 33846365258     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.011909     Document Type: Article

References (63)

1. E. Basar, Brain Function and Oscillations I: Brain Oscillations. Principles and Approaches (Springer-Verlag, Berlin, 1998).
2. H. Haken, Brain Dynamics-Synchronization and Activity Patterns in Pulse-Coupled Neural Nets with Delays and Noise (Springer-Verlag, Berlin, 2002).
3. B. Lindner, J. Garcia-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2003.10.015 392, 321 (2004).
4. Q. Y. Wang, Q. S. Lu, G. R. Chen, and D. H. Guo, Phys. Lett. A PYLAAG 0375-9601 356, 17 (2006).
5. C. M. Gray, P. König, A. K. Engel, and W. Singer, Nature (London) NATUAS 0028-0836 10.1038/338334a0 338, 334 (1989).
6. R. Eckhorn, A. Frien, R. Bauer, T. Woelbern, and H. Kehr, NeuroReport NERPEZ 0959-4965 4, 243 (1993).
7. A. K. Kreiter and W. Singer, J. Neurosci. JNRSDS 0270-6474 16, 2381 (1996).
8. D. Golomb and J. Rinzel, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94) 90214-3 72, 259 (1994).
9. N. Brunel, J. Physiol. (London) JPHYA7 0022-3751 94, 445 (2000).
10. G. Mongillo and D. J. Amit, J. Comput. Neurosci. JCNEFR 0923-5313 11, 249 (2001).
11. W. Gerstner and W. M. Kistler, Spiking Neuron Models. Single Neurons, Populations, Plasticity (Cambridge University Press, Cambridge, England, 2002).
12. A. Karantonis, Y. Miyakita, and S. Nakabayashi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.046213 65, 046213 (2002).
13. Y. Miyakita, A. Karantonis, and S. Nakabayashi, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(02)01054-0 362, 461 (2002).
14. N. Brunel, V. Hakim, and M. J. E. Richardson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.051916 67, 051916 (2003).
15. D. T. W. Chik and Z. D. Wang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.031907 68, 031907 (2003).
16. A. Di Garbo, M. Barbi, and S. Chillemi, BioSystems BSYMBO 0303-2647 67, 45 (2002).
17. M. Nomura, T. Fukai, and T. Aoyagi, Neural Comput. NEUCEB 0899-7667 15, 2179 (2003).
18. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London) JPHYA7 0022-3751 117, 500 (1952).
19. J. A. Connor, D. Walter, and R. McKown, Biophys. J. BIOJAU 0006-3495 18, 81 (1977).
20. C. Morris and H. Lecar, Biophys. J. BIOJAU 0006-3495 35, 193 (1981).
21. T. R. Chay and J. Keizer, Biophys. J. BIOJAU 0006-3495 42, 181 (1983).
22. L. Lapicque, J. Physiol. Pathol. Gen. JPPGAR 0368-3834 9, 620 (1907).
23. R. FitzHugh, Biological Engineering, edited by H. P. Schwan (McGraw-Hill, New York, 1969), p. 1.
24. T. Yanagita, T. Ichinomiya, and Y. Oyama, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.056218 72, 056218 (2005).
25. H. P. McKean, Adv. Math. ADMTA4 0001-8708 10.1016/0001-8708(70)90023-X 4, 209 (1970).
26. D. Hansel, G. Mato, and C. Meunier, Neural Comput. NEUCEB 0899-7667 7, 307 (1995).
27. G. B. Ermentrout, Neural Comput. NEUCEB 0899-7667 8, 979 (1996).
28. R. G. Kavasseri, Proceedings of the Hawaii International Conference on Sciences Honolulu, 2004.
29. J. Keener and J. Sneyd, Mathematical Physiology (Springer-Verlag, New York, 1998).
30. A. Longtin, Chaos CHAOEH 1054-1500 10.1063/1.166140 5, 209 (1995).
31. R. E. Mirollo and S. H. Strogatz, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0150098 50, 1645 (1990).
32. C. Van Vreeswijk, L. F. Abbott, and G. B. Ermentrout, J. Comput. Neurosci. JCNEFR 0923-5313 1, 1313 (1994).
33. C. C. Chen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.2668 49, 2668 (1994).
34. V. Kirk and E. Stone, Phys. Lett. A PYLAAG 0375-9601 232, 70 (1997).
35. C. C. Chow and N. Kopell, Neural Comput. NEUCEB 0899-7667 10.1162/089976600300015295 12, 1643 (2000).
36. Y. D. Sato, Phys. Lett. A PYLAAG 0375-9601 319, 486 (2003).
37. A. Tonnelier and W. Gerstner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.021908 67, 021908 (2003).
38. D. Somers and N. Kopell, Biol. Cybern. BICYAF 0340-1200 10.1007/BF00198772 68, 393 (1993).
39. S. Coombes, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(01)00352-9 160, 173 (2001).
40. M. Denman-Johnson and S. Coombes, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.051903 67, 051903 (2003).
41. D. Terman and D. L. Wang, Physica D PDNPDT 0167-2789 10.1016/0167- 2789(94)00205-5 81, 148 (1995).
42. X. J. Wang and G. Buzsáki, J. Neurosci. JNRSDS 0270-6474 16, 6402 (1996).
43. H. R. Wilson, Spikes, Decisions, and Actions-The Dynamical Foundations of Neuroscience (Oxford University Press, New York, 1999).
44. G. Renversez, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00149-8 114, 114 (1998).
45. A. Bose, N. Kopell, and D. Terman, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00232-8 140, 69 (2000).
46. Y. D. Sato and M. Shiino, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.041903 66, 041903 (2002).
47. S. R. Campbell, D. L. Wang, and C. Jayaprakash, IEEE Trans. Neural Netw. ITNNEP 1045-9227 10.1109/TNN.2004.833134 15, 1027 (2004).
48. J. C. Neu, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0137022 37, 307 (1979).
49. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
50. F. C. Hoppensteadt and E. M. Izhikevich, Weakly Connected Neural Networks (Springer-Verlag, Berlin, 1997).
51. E. M. Izhikevich, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139999351001 60, 1789 (2000).
52. G. B. Ermentrout and N. Kopell, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0150009 50, 125 (1990).
53. P. Frankel and T. Kiemel, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0153067 53, 1436 (1993).
54. P. R. Adams, S. W. Jones, P. Pennefather, D. A. Brown, C. Koch, and C. Lancaster, J. Exp. Biol. JEBIAM 0022-0949 124, 259 (1986).
55. D. Kleinfeld, F. Raccuia-Behling, and H. J. Chiel, Biophys. J. BIOJAU 0006-3495 57, 697 (1990).
56. N. I. Syed, G. M. Bulloch, and K. Lukowiak, Science SCIEAS 0036-8075 250, 282 (1990).
57. L. F. Abbott and T. B. Kepler, in Statistical Mechanics of Neural Networks, Lecture Notes in Physics Vol. 368, edited by, L. Garrido, (Springer-Verlag, Berlin, 1990), p. 5.
58. D. T. W. Chik, S. Coombes, and Z. D. Wang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.011908 70, 011908 (2004).
59. G. B. Ermentrout and C. C. Chow, Physiol. Behav. PHBHA4 0031-9384 77, 629 (2002).
60. C. van Vreeswijk, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.5522 54, 5522 (1996).
61. P. C. Bressloff and S. Coombes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.2168 81, 2168 (1998).
62. Y. D. Sato, Ph.D. thesis, Tokyo Institute of Technology, 2005 (unpublished).
63. B. Ermentrout, Neural Comput. NEUCEB 0899-7667 15, 2483 (2003).