Entrainment in pacemakers characterized by a V-shaped PRC

Journal of Mathematical Biology
C Torras i Genís

Abstract

The behaviour of a class of pacemakers characterized by a V-shaped PRC has been determined, for all possible frequencies and amplitudes of stimulation. The analytical study of the phase transition equation reveals that all rhythmic stimuli, but for a set of measure zero, give rise to entrainment. The ratio between firing and stimulation frequencies is a generalized Cantor function of the ratio between spontaneous and stimulation frequencies. A procedure to compute the detailed input/output pattern that underlies each entrainment ratio is given. Finally, the neurophysiological assumptions and implications of the results obtained are discussed.

References

May 15, 1979·Journal of Mathematical Biology·L Glass, M C Mackey
Jan 1, 1985·Biological cybernetics·C Torras i Genís
Mar 1, 1972·Kybernetik·J Nagumo, S Sato
Jun 1, 1972·The Journal of General Physiology·B W Knight
Jan 1, 1982·Journal of Mathematical Biology·F C Hoppensteadt, J P Keener
Jan 1, 1982·Biological cybernetics·S YoshizawaJ Nagumo
Oct 7, 1980·Journal of Theoretical Biology·L GlassM C Mackey
Dec 12, 1964·Nature·R M HOWELLG B SCOTT

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Citations

Jan 1, 1987·Biological cybernetics·C Torras i Genís
Jan 1, 1985·Biological cybernetics·C Torras i Genís
Mar 9, 2004·Chaos·Mark McGuinnessPeter Larsen
Nov 13, 1995·Physical Review Letters·Á CorralA Arenas
Apr 15, 1990·Physical Review. a·J RinglandM Schell
Aug 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A Arenas, Pérez Vicente CJ

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