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

Bin Zhang; Xiaofang Zhang; Wenan Jiang; Hu Ding; Liqun Chen; Qinsheng Bi

doi:10.1016/j.cnsns.2022.106806

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

Bin Zhang
, Xiaofang Zhang
, Wenan Jiang^*
, Hu Ding
, Liqun Chen
, Qinsheng Bi

^*Corresponding author for this work

Jiangsu University
Shanghai University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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.

Original language	English
Article number	106806
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	116
DOIs	https://doi.org/10.1016/j.cnsns.2022.106806
State	Published - Jan 2023
Externally published	Yes

Keywords

Bursting oscillations
Coexisting attractors
Domain of attraction
Multiple stability

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10.1016/j.cnsns.2022.106806

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

abstract = "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.",

keywords = "Bursting oscillations, Coexisting attractors, Domain of attraction, Multiple stability",

author = "Bin Zhang and Xiaofang Zhang and Wenan Jiang and Hu Ding and Liqun Chen and Qinsheng Bi",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

month = jan,

doi = "10.1016/j.cnsns.2022.106806",

language = "英语",

volume = "116",

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TY - JOUR

T1 - Bursting oscillations induced by multiple coexisting attractors in a modified 3D van der Pol-Duffing system

AU - Zhang, Bin

AU - Zhang, Xiaofang

AU - Jiang, Wenan

AU - Ding, Hu

AU - Chen, Liqun

AU - Bi, Qinsheng

PY - 2023/1

Y1 - 2023/1

N2 - 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.

AB - 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.

KW - Bursting oscillations

KW - Coexisting attractors

KW - Domain of attraction

KW - Multiple stability

UR - https://www.scopus.com/pages/publications/85137744241

U2 - 10.1016/j.cnsns.2022.106806

DO - 10.1016/j.cnsns.2022.106806

M3 - 文章

AN - SCOPUS:85137744241

SN - 1007-5704

VL - 116

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 106806

ER -

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

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Keywords

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