Some principles and paradoxes about the phase control of biological oscillations∗

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Abstract
Stable, self‐sustaining oscillations respond to a stimulus in very complicated ways; but they typically regulate back to normal oscillation with only a phase shift remaining to distinguish the disturbed oscillator from an undistrubed control. The new phase (latent, if not immediately expressed, at the moment the stimulus ends) depends on an old phase and a stimulus magnitude. Graphed, this dependence typically resembles one turn of a screw surface, repeated periodically along both the old phase axis and the new phase axis. This 3‐dimensional graph summarizes pictorially several “rules of phase control”. Their range of application seems to include several biologically interesting rhythms.