Eur. Phys. J. Plus (2021) 136: 998
https://doi.org/10.1140/epjp/s13360-021-01970-3

Regular Article

A novel bursting oscillation and its transitions in a modified Bonhoeffer–van der Pol oscillator with weak periodic excitation

Faculty of Civil Engineering and Mechanics, Jiangsu University, 212013, Zhenjiang, People’s Republic of China

^d xjhan@ujs.edu.cn

Received: 21 May 2020
Accepted: 16 September 2021
Published online: 5 October 2021

Abstract

In this paper, we investigate the bursting dynamics in a modified Bonhoeffer–van der Pol oscillator with weak periodic excitation. First, by regarding the weak periodic excitation as a slow-varying parameter, the stabilities and bifurcations of the fast subsystem are obtained. Based on that, a new bursting pattern named compound “subHopf/Sacker” type is investigated by taking advantage of the fast–slow research technology. Then, with the help of the two-parameter bifurcation analysis, the dynamical transitions of the compound bursting are presented, and the other two compound bursting types, i.e., compound “subHopf/fold-cycle” bursting and compound “supHopf/supHopf” bursting, are proposed. We find that different types of bifurcations can be observed in two narrow parameter intervals, and these bifurcations are most sensitive to the change of parameter k₃. Our results provide a new possible route to bursting behaviors, and the reliability of this research is tested and verified by the superposition of the slow manifold on the plane of (δ, x) and bifurcation diagram.