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 particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcations. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium.
bifurcation modified bvp equation homoclinic orbit chaos neuronal model