Bifurcation mechanism of doubly nested mixed-mode oscillations

Abstract

Doubly nested mixed-mode oscillations (MMOs) have been observed in a driven classical Bonhoeffer-van der Pol oscillator. However, the bifurcation phenomena surrounding doubly nested MMOs have not yet been clarified. In this study, we investigated the bifurcation phenomena of doubly nested MMOs. A one-parameter bifurcation diagram and phase planes were used to confirm the circuit behavior around the bifurcation points. First-return maps were then used to show the effects of bifurcation phenomena on sequences of doubly nested MMOs. The composite first-return map qualitatively explains the bifurcation mechanism that causes doubly nested MMOs.