Beyond a pacemaker's entrainment limit: Phase walk-through

G. B. Ermentrout, J. Rinzel

Research output: Contribution to journalArticlepeer-review


Desynchronization occurs when a pacemaker is externally stimulated at too high a rate, beyond the entrainment limit. One may then observe phase walk-through: the pacemaker and stimulus phase difference, rather than lock to a fixed pattern, may cycle repeatedly through all values. By means of a simple but nonlinear one-variable model we describe qualitatively the properties of entrainment, loss of entrainment, and phase walk-through for rhythmically stimulated pacemakers. We obtain an expression for the cycle length (beat period) of the repetitive phase walk-through. This shows, in contrast to the simplest treatment, that in general beat frequency is not a simple linear function of the difference between the pacemaker and stimulus frequencies. Our results are illustrated in the context of a model experimental pacemaker, the rhythmically flashing firefly. We discuss how these modeling results apply in a much more general setting.

Original languageEnglish (US)
Pages (from-to)R102-R106
JournalThe American journal of physiology
Issue number1 Pt 2
StatePublished - 1984

ASJC Scopus subject areas

  • Physiology


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