COLLECTIVE SYNCHRONIZATION OF PULSE-COUPLED OSCILLATORS AND EXCITABLE UNITS

A phase model is proposed and studied for a population of integrate-and-fire-type oscillators and excitable units with pulsatile coupling. The units are subject to external noise, and their mutual connection is all-to-all. An evolution equation is derived for the phase distribution in a closed form. Its steady-state analysis in the limit of weak noise shows the possibility of collective bistability. The evolution equation is simplified drastically when the coupling as well as noise is sufficiently weak. This reduction of equation enables analytical calculation of various quantities. Among others, the stability of the steady distribution is analyzed explicitly, and the onset of collective oscillations is described in terms of the Hopf bifurcation. It is also shown that the present model is improved in some respects by introducing absolute refractoriness.