Bursting Oscillations in Nonlinear Oscillators With Slowly Varying Excitation

Abstract

This work represents the extension of a recently published paper by the authors, where mechanical manifestations of bursting oscillations in slowly rotating systems are presented. One of these mechanical systems consists of a mass moving along a slowly rotating frame, which creates a slowly varying external excitation. Here, the aim is to link its mathematical model with Izhikevich’s methodology and classification for bursting oscillations. In this respect, the existence of a ’fold – fold’ hysteresis loop of a point-point type burster is recognised and explained in detail. Thus, in the system considered, bursting oscillations occur becouse the rate of convergence between the branches of the slow flow is relatively weak. The influence of some system’s parametrs on the characteristics of fast motion is illustrated.