Abstract.
We investigate how firing activity of complex neural networks depends on the random long-range connections and coupling strength. Network elements are described by excitable space-clamped FitzHugh-Nagumo (SCFHN) neurons with the values of parameters at which no firing activity occurs. It is found that for a given appropriate coupling strength C, there exists a critical fraction of random connections (or randomness) p*, such that if p > p* the firing neurons, which are absent in the nearest-neighbor network, occur. The firing activity becomes more frequent as randomness p is further increased. On the other hand, when the p is smaller, there are no active neurons in network, no matter what the value of C is. For a given larger p, there exist optimal coupling strength levels, where firing activity reaches its maximum. To the best of our knowledge, this is a novel mechanism for the emergence of firing activity in neurons.
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References
M.E.J. Newman, J. Stat. Phys. 101, 819 (2000)
S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, UK, 2003)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
A.D. Sánchez, J.M. Lpoez, M.A. Rodríguez, Phys. Rev. Lett. 88, 048701 (2002)
S. Yonker, R. Wackerbauer, Phys. Rev. E 73, 026218 (2006)
D.Q. Wei, X.S. Luo, Europhys. Lett. 78, 68004 (2007)
M. Dhamala, V.K. Jirsa, M.Z. Ding, Phys. Rev. Lett. 92, 028101 (2004)
O. Kwon, H.-H. Jo, H.-T. Moon, Phys. Rev. E 72, 066121 (2005)
Q.S. Li, Y. Liu, Phys. Rev. E 73, 016218 (2006)
O. Shefi, I. Golding, R. Segev, E. Ben-Jacob, A. Ayali, Phys. Rev. E 66, 021905 (2002)
C.J. Stam, Neurosci. Lett. 355, 25 (2004)
L.M.A. Bettencourt, G.J. Stephens, M.I. Ham, G.W. Gross, Phys. Rev. E 75, 021915 (2007)
A. Roxin, H. Riecke, S.A. Solla, Phys. Rev. Lett. 92, 198101 (2004)
T. Shimokawa, S. Shinomoto, Phys. Rev. E 73, 066221 (2006)
T. Nowotny, M.I. Rabinovich, Phys. Rev. Lett. 98, 128106 (2007)
R. Fitzhugh, Biophys. J. 1, 445 (1961)
J.S. Nagumo, S. Arimoto, S. Yoshizawa, Proc. IRE 50, 2061 (1962)
F. Qi, Z.H. Hou, H.W. Xin, Phys. Rev. Lett. 91, 064102 (2003)
A. Tonnelier, Siam J. Appl. Math. 63, 459 (2002)
Y.H. Gao, Chaos, Solitons & Fractals 21, 943 (2004)
M.H. Chou, Comput. Math. Applic. 29, 19 (1995)
M.H. Chou, Y.T. Lin, Comput. Math. Applic. 32, 109 (1996)
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Wei, D., Luo, X. & Zou, Y. Firing activity of complex space-clamped FitzHugh-Nagumo neural networks. Eur. Phys. J. B 63, 279–282 (2008). https://doi.org/10.1140/epjb/e2008-00227-5
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DOI: https://doi.org/10.1140/epjb/e2008-00227-5