Bursting oscillations induced by multiple coexisting attractors in a modified 3D van der Pol-Duffing system

In this paper, a novel three-dimensional modified van der Pol-Duffing circuit with a quintic nonlinear resistor is proposed, and the multiple stable attractors are observed. The complex bursting patterns are investigated, various patterns of bursting oscillations are obtained under slowly changing frequency, and the transition mechanism of which can be revealed via the modified slow-fast analysis as well as the transformed phase portrait. It can be found that for the system with mono-stability, only one bursting pattern exists, while for the case with multi-stability, the trajectory can enter into different attraction areas in the transition region, leading to complex forms of bursting oscillations. Furthermore, the multi-valued characteristic of the system are observed by the domain of attraction. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a novel three-dimensional modified van der Pol-Duffing circuit with a quintic nonlinear resistor, and multiple stable attractors are observed. The complex bursting patterns are investigated, and various patterns of bursting oscillations are obtained under slowly changing frequency, revealing the transition mechanism.