RT Journal Article
T1 Spiking behavior in a noise-driven system combining oscillatory and excitatory properties
A1 Makarov Slizneva, Valeriy
A1 Nekorkin, Vladimir I.
A1 Velarde, Manuel G.
AB We show that firing activity (spiking) can be regularized by noise in a FitzHugh-Nagumo (FHN) neuron model when operating slightly beyond the supercritical Hopf bifurcation (in the "canard" region). We also provide the conditions for imperfect phase Locking between interspike intervals and low amplitude quasiharmonic oscillations. For the imperfect phase locking no need exists of an external signal as it follows from the FHN intrinsic dynamics.
PB American Physical Society
SN 0031-9007
YR 2001
FD 2001-04-09
LK https://hdl.handle.net/20.500.14352/57693
UL https://hdl.handle.net/20.500.14352/57693
LA eng
NO R. Llinas and Y. Yarom, J. Physiol. 376, 163 (1986) .L. S. Benardo and R. E. Foster, Brain Res. Bull. 17, 773 (1986) .K. Sasaki, J. M. Bower, and R. Llinas, Eur. J. Neurosci. 1, 572 (1989).J. J. Collins, T. T. Imhoff, and P. Grigg, Nature (London) 383, 770 (1996) .R. M. Siegel, Physica (Amsterdam) 42D, 385 (1990).H. Haken, Principles of Brain Functioning (Springer-Verlag, Berlin,1996).R. FitzHugh, Biophys. J. 1, 445 (1961) .F. C. Hoppensteadt, An Introduction to the Mathematics of Neurons (Cambridge Univ. Press, NY,1986).K. Wiesenfeld, D. Pierson, E. Pantazelou, C. Dames, and F. Moss, Phys. Rev. Lett. 72, 2125 (1994) .J. J. Collins, C. C. Chow, and T. T. Imhoff, Phys. Rev. E 52, R3321 (1995) .J. Milton, Dynamics of Small Neural Populations (American Math. Soc., Providence, Rhode Island,1996).A. Longtin, Phys. Rev. E 55, 868 (1997).C. Eichwald and J. Walleczek, Phys. Rev. E 55, R6315 (1997) .A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. 78, 775 (1997) .S. G. Lee, A. Neiman, and S. Kim, Phys. Rev. E 57, 3292 (1998) .J. P. Baltanas and J. M. Casado, Physica (Amsterdam) 122D, 231 (1998).C. Hauptmann, F. Kaiser, and C. Eichwald, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 1159 (1999).R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 14, L453 (1981).C. Nicolis and G. Nicolis, Tellus 33, 225 (1981).L. Gammaitoni, P. Hanggi, D. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) .R. R. Llinas and K. D. Walton, in The Synaptic Organization of the Brain,G. M. Shepherd (Oxford Univ. Press, Oxford,1998), Chap. 7.F. Dumortier, in Bifurcations and Periodic Orbits of Vector Fields,D. Schlomiuk (Kluwer Academic Press, Dordrecht,1993), pp. 19–73.P. Glendinning, Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge Univ. Press, NY,1994), Chap. 8.10.R. F. Fox, I. R. Gatland, R. Roy, and G. Vemuri, Phys. Rev. A 38, 5938 (1988) .J. M. Kowalski, G. L. Albert, B. K. Rhoades, and G. W. Gross, Neural Netw. 5, 805 (1992).Y. Manor, J. Rinzel, I. Segev, and Y. Yarom, J. Neurophysiol. 77, 2736 (1997) .
NO Spanish Ministry of Science and Technology
NO Programa Catedra of the BBV Foundation (Spain)
NO Russian Foundation
DS Docta Complutense
RD 29 abr 2024