1. Repetitive firing in space‐clamped squid axons bathed in low Ca and stimulated by a just suprathreshold step of current can be annihilated by a brief depolarizing or hyperpolarizing pulse of the proper magnitude applied at the proper phase. 2. In response to such perturbations, membrane potential and ionic currents show damped oscillations toward a steady state. 3. For other, non‐annihilating, perturbations repetitive firing resumes with unaltered frequency but with phase resetting. 4. Experimental findings are compared with calculations for the space‐and current‐clamped Hodgkin‐Huxley equations. Annihilation of repetitive firing to a steady state corresponds to a solution trajectory perturbed off a stable limit cycle and into the domain of attraction of a coexistent stable singular point. 5. Experimentally and theoretically the nerve exhibits hysteresis with two different stable modes of operation for a just suprathreshold range of bias current: the oscillatory repetitive firing state and the time‐independent steady state. 6. Analogy is made to a brief synaptic input (excitatory or inhibitory) which may start or stop a biological pace‐maker.
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