New Bursting Patterns in the Lü System Driven by Orthogonal Parametric Excitation and External Excitation

Abstract

Compared with the general nonlinear system, multi-timescale system has complex dynamical characteristics of bursting oscillations, which has received extensive attention. This paper aims to show and study the bursting oscillations and bifurcation phenomena in the Lü systems driven by orthogonal parametric excitation and external excitation. By using the fast–slow analysis, we were able to get two different fast subsystems corresponding to different bifurcation diagrams when the slow variable increased and decreased. Several novel bursting modes have been discovered, namely, delayed supHopf/cascaded with PD and IPD/Fold/cascaded with PD and IPD/supHopf-Fold bursting, delayed supHopf/supHopf/Fold-Fold bursting and delayed supHopf/cascaded with PD and IPD/supHopf-Fold bursting. Finally, a simulation circuit of the multi-timescale system is established in Multisim, and a real physical circuit is also built. The experimental results effectively verify the research results.