Piecewise-linear Bonhoeffer-van der Pol dynamics explaining mixed-mode oscillation-incrementing bifurcations

Abstract

This study investigates mixed-mode oscillations (MMOs) generated by weakly driven piecewiselinear Bonhoeffer-van der Pol and Fitzhugh-Nagumo dynamics. Such a simple piecewise-linear oscillator can generate extremely complex MMO bifurcations such as mixed-mode oscillationincrementing bifurcations (MMOIBs) and intermittently chaotic MMOs. These remarkable bifurcations are confirmed using explicit solutions of the piecewise-linear differential equation. Moreover, Lorenz plots are introduced, which strongly suggest that MMOIBs occur successively many times, and show that each MMO sequence is surrounded by chaos.