Locking, intermittency, and bifurcations in a periodically driven pacemaker neuron: Poincaré maps and biological implications.

Slowly adapting stretch receptor (SAO) pacemaker neurons, driven with periodic tugs, were analyzed by way of Poincaré mappings (Appendix). Two behaviors were apparent. i) Intermittency characterized previously unclear situations: discharges shifted irregularly between prolonged epochs where spike phases (relative to tugs) and intervals barely changed (slid), and brief bursts with marked variations (skipped). ii) Locking was well-known: phases and intervals remained almost fixed, regardless of the initiation. Changing frequencies, map domains with locking (ordered according to spikes/tugs ratios), alternated with intermittent ones. The best fit for any experimental map was a curve, not straight but certainly unidimensional, continuous and monotonic; it varied characteristically with frequency. This suggested relations called diffeomorphisms, implying periodicity and quasi-periodicity. Outcomes, expanding previous knowledge and meaningful biologically, were i) a precise, exhaustive behavior list (including between behavior transitions) and ii) a thorough understanding or model. This, in turn, provides norms for more specific models (single-variable ones suffice), constraints upon basic mechanisms (one variable, reflecting several real ones combined, should behave as the phase), and forecasts for future experimentation (e.g., unexamined tug frequencies and amplitudes).