Chaos disappearance in a piecewise linear Bonhoeffer–van der Pol dynamics with a bistability of stable focus and stable relaxation oscillation under weak periodic perturbation

Abstract

This study elucidates the bifurcation structure causing chaos disappearance in a four-segment piecewise linear Bonhoeffer–van der Pol oscillator with a diode under a weak periodic perturbation. The parameter values of this oscillator are chosen such that stable focus and stable relaxation oscillation can coexist in close proximity in the phase plane if no perturbation is applied. Chaos disappearance occurs through a previously unreported novel and unconventional bifurcation mechanism. To rigorously analyze these phenomena, the diode in this oscillator is assumed to operate as a switch. In this case, the governing equation is represented as a constraint equation, and the Poincare map is constructed as an one-dimensional map. By analyzing the Poincare map, we clearly demonstrate why the stable relaxation oscillation that exists when no perturbation is applied disappears via chaotic oscillation when an extremely weak perturbation is applied.