Bursting oscillations and mechanism analysis in a non-smooth Duffing system with frequency domain of two time scales

Abstract

The main purpose of the manuscript is to explore the bursting oscillations in a dynamic system with non-smooth factor. Take the duffing system as a example, by introducing dry friction, and choosing periodic excitation ensure that there exists order gap between the natural frequency and the exited frequency, a non-smooth system with two time scales is established. The whole exciting term can be regarded as a slow-varying parameter, which leads to the generalized autonomous system, and the stability and the associated bifurcation conditions can be derived. By taking suitable parameter values, three typical cases are considered under the three group different parameters which can described as double scrolls, three scrolls and four scrolls. By using the transformed phase portrait and considering the effect of non-smooth factor, the associated bifurcation mechanism of the bursting oscillations is discussed, which may reveal different forms of bursting oscillations and transition mechanism between quiescent states and the spiking states. In addition, aiming at the coexistence of multiple equilibrium states in this non-smooth system, combined with the influence of evolution behavior of the attractor itself, and further reveals that the reason for showing special oscillation phenomena under the influence of non-smooth factor.