DYNAMICAL BEHAVIORS OF VAN DER POL-DUFFING SYSTEMS WITH INDEFINITE DEGREE

被引：3
|
作者：
Chen, Hebai [1 ]
Feng, Zhaosheng [2 ]
Li, Zhijie [1 ]
Wang, Zhaoxia [3 ]
机构：
[1] Cent South Univ, Sch Math & Stat, HNP LAMA, Changsha 410083, Hunan, Peoples R China
[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA
[3] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2024年 / 44卷 / 01期
关键词：
Van der Pol-Duffing oscillator; indefinite degree; bifurcation; global; phase portrait; Poincare disc; limit cycle; figure-eight loop; LIENARD EQUATIONS; OSCILLATOR;
D O I：
10.3934/dcds.2023104
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study dynamical behaviors of van der Pol-Duffing oscillator systems with indefinite degree. Under certain conditions, we show some novel and rich complex dynamics, including abundant nonlinear phenomena such as three limit cycles, figure-eight loop, global phase portraits, and infinitely many heteroclinic bifurcation surfaces.
引用
收藏
页码：281 / 317
页数：37
相关论文
共 50 条
  • [1] A van der Pol-Duffing Oscillator with Indefinite Degree
    Chen, Hebai
    Jin, Jie
    Wang, Zhaoxia
    Zhang, Baodong
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2022, 21 (04)
  • [2] A van der Pol-Duffing Oscillator with Indefinite Degree
    Hebai Chen
    Jie Jin
    Zhaoxia Wang
    Baodong Zhang
    Qualitative Theory of Dynamical Systems, 2022, 21
  • [3] Bifurcations of the van der Pol-Duffing oscillator
    Pusenjak, R
    STROJNISKI VESTNIK-JOURNAL OF MECHANICAL ENGINEERING, 2003, 49 (7-8): : 370 - 384
  • [4] On Coupled Delayed Van der Pol-Duffing Oscillators
    Pandey, Ankan
    Mitra, Mainak
    Ghose-Choudhury, A.
    Guha, Partha
    JOURNAL OF APPLIED NONLINEAR DYNAMICS, 2020, 9 (04) : 567 - 574
  • [5] On the dynamics of a Van der Pol-Duffing snap system
    Wiggers, Vinicius
    Rech, Paulo C.
    EUROPEAN PHYSICAL JOURNAL B, 2022, 95 (02):
  • [6] Horseshoe in a modified Van der Pol-Duffing circuit
    Fan, Qing-ju
    APPLIED MATHEMATICS AND COMPUTATION, 2009, 210 (02) : 436 - 440
  • [7] On bifurcations and chaos in the Van der Pol-Duffing oscillator
    Bykov, VV
    RADIOTEKHNIKA I ELEKTRONIKA, 1997, 42 (09): : 1084 - 1096
  • [8] VAN DER POL-DUFFING MODELING FOR TORSIONAL GALLOPING
    Fernandes, Antonio Carlos
    Armandei, Mohammadmehdi
    33RD INTERNATIONAL CONFERENCE ON OCEAN, OFFSHORE AND ARCTIC ENGINEERING, 2014, VOL 9B: OCEAN RENEWABLE ENERGY, 2014,
  • [9] FREQUENCY RESPONSE OF A VAN DER POL-DUFFING OSCILLATOR
    HAAS, VB
    PROCEEDINGS OF THE INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, 1971, 59 (02): : 334 - &
  • [10] Analytical solution for Van der Pol-Duffing oscillators
    Kimiaeifar, A.
    Saidi, A. R.
    Bagheri, G. H.
    Rahimpour, M.
    Domairry, D. G.
    CHAOS SOLITONS & FRACTALS, 2009, 42 (05) : 2660 - 2666
12345