Reverberating activity in a neural network with distributed signal transmission delays

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

Volumn 76, Issue 5, 2007, Pages

  Omi, Takahiro ^a   Shinomoto, Shigeru ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC LINES; POWER TRANSMISSION; SYSTEMS ANALYSIS; TIME DELAY;

DISTRIBUTED SIGNAL TRANSMISSION DELAY; REVERBERATING ACTIVITY; TRANSMISSION DELAY;

NEURAL NETWORKS;

EID: 36048996863     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.051908     Document Type: Article

References (42)

1. H. R. Wilson and J. D. Cowan, Biophys. J. BIOJAU 0006-3495 12, 1 (1972).
2. S. Amari, IEEE Trans. Syst. Man Cybern. ISYMAW 0018-9472 2, 643 (1972).
3. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
4. H. Sakaguchi, S. Shinomoto, and Y. Kuramoto, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.77.1005 77, 1005 (1987).
5. W. Gerstner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.738 51, 738 (1995).
6. T. Shimokawa and S. Shinomoto, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.066221 73, 066221 (2006).
7. M. Y. Choi and B. A. Huberman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.2862 31, 2862 (1985).
8. C. M. Marcus and R. M. Westervelt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.347 39, 347 (1989).
9. S. Sano, A. Uchida, S. Yoshimori, and R. Roy, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.016207 75, 016207 (2007).
10. M. N. Oǧuztöreli, Time-Lag Control Systems (Academic Press, New York, 1966).
11. H. A. Swadlow, J. Neurophysiol. JONEA4 0022-3077 54, 1346 (1985).
12. J. G. Pelletier and D. Paré, J. Neurophysiol. JONEA4 0022-3077 87, 1213 (2002).
13. A. F. Soleng, M. Raastad, and P. Andersen, Hippocampus HIPPEL 1050-9631 13, 953 (2003).
14. J. Foss and J. Milton, J. Neurophysiol. JONEA4 0022-3077 84, 975 (2000).
15. J. Ma and J. Wu, Neural Comput. NEUCEB 0899-7667 10.1162/neco.2007.19.8. 2124 19, 2124 (2007).
16. S. Amari, Proc. IEEE IEEPAD 0018-9219 59, 35 (1971).
17. S. Shinomoto, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.75.1313 75, 1313 (1986).
18. W. Kinzel, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01304440 60, 205 (1985).
19. S. Shinomoto, Biol. Cybern. BICYAF 0340-1200 10.1007/BF00364151 57, 197 (1987).
20. K. E. Kürten, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(88) 90135-1 129, 157 (1988).
21. E. Greenfield and H. Lecar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.041905 63, 041905 (2001).
22. P. C. McGuire, Neural Networks NNETEB 0893-6080 10.1016/S0893-6080(02) 00087-4 15, 1243 (2002).
23. S. Bornholdt and T. Röhl, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066118 67, 066118 (2003).
24. N. Bertschinger and T. Natschläger, Neural Comput. NEUCEB 0899-7667 10.1162/089976604323057443 16, 1413 (2004).
25. L. I. Rozonoér, Autom. Remote Control (Engl. Transl.) AURCAT 0005-1179 5, 773 (1969).
26. S. Amari, K. Yoshida, and K. Kanatani, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0133008 33, 95 (1977).
27. N. MacDonald, Biological Delay Systems: Linear Stability Theory (Cambridge University Press, New York, 1989).
28. K. Ikeda and K. Matsumoto, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90058-3 29, 223 (1987).
29. J. Losson, M. C. Mackey, and A. Longtin, Chaos CHAOEH 1054-1500 10.1063/1.165982 3, 167 (1993).
30. J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.708 76, 708 (1996).
31. J. Cao and J. Wang, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. ITCAEX 1057-7122 10.1109/TCSI.2002.807494 50, 34 (2003).
32. S. Mohamad and K. Gopalsamy, Appl. Math. Comput. AMHCBQ 0096-3003 10.1016/S0096-3003(01)00299-5 135, 17 (2003).
33. S. Arik, Neural Networks NNETEB 0893-6080 10.1016/j.neunet.2004.02.001 17, 1027 (2004).
34. V. K. Jirsa and M. Ding, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.070602 93, 070602 (2004).
35. Q. Zhang, X. Wei, and J. Xu, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/j.chaos.2005.05.026 28, 331 (2006).
36. A. Knoblauch and F. T. Sommer, Neurocomputing NRCGEO 0925-2312 52-54, 301 (2003).
37. E. M. Izhikevich, Neural Comput. NEUCEB 0899-7667 10.1162/ 089976606775093882 18, 245 (2006).
38. P. Gong and C. van Leeuwen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.048104 98, 048104 (2007).
39. K. Pyragas, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90745-8 170, 421 (1992).
40. T. Hikihara and T. Kawagoshi, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(96)00560-9 221, 29 (1996).
41. K. Höhne, H. Shirahama, C. U. Choe, H. Benner, K. Pyragas, and W. Just, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.214102 98, 214102 (2007).
42. I. Z. Kiss, C. Rusin, H. Kori, and J. L. Hudson, Science SCIEAS 0036-8075 10.1126/science.1140858 316, 1886 (2007).