Bifurcation of a modified BVP circuit model for neurons generating rectangular waves

We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhoffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particula r, we clarify a mechanism of properties in a one-parameter graph on the per iod of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcati ons. The occurrence of homoclinic bifurcations is confirmed by using the li nking number of limit cycles related with the stable manifold through an eq uilibrium.