Chaotic bursting patterns induced by transient chaos in a smooth three-dimensional dynamic model

Abstract

This paper aims to report the transient-chaos-induced chaotic bursting oscillations in a smooth three-dimensional dynamic model with a low-frequency excitation when an order gap exists between the excitation frequency and the natural frequency. Based on the Nosé-Hoover system, a periodically driven nonlinear system is modelled, in which the transient chaos induced by boundary crisis route can be observed. Through theoretical analysis and numerical simulation, the stability conditions of the equilibrium point and six transient-chaos-induced chaotic bifurcation structures are obtained. Six typical cases in which different routes of the trajectories pass through the transient chaos areas, leading to different patterns of bursting oscillations. It can be found that not only the bifurcation structures but also the bifurcation delay behavior can influence the bursting patterns. In addition, in the transient chaos areas, the bifurcation delay behavior can result in the disappearance of the periodic signals in the small periodic windows.