Coexistence of Periodic, Chaotic and Hyperchaotic Attractors in a System Consisting of a Duffing Oscillator Coupled to a van der Pol Oscillator

被引:9
|
作者
Tanekou, Sosthene Tsamene [1 ]
Ramadoss, Janarthanan [2 ]
Kengne, Jacques [3 ]
Kenmoe, Germaine Djuidje [4 ]
Rajagopal, Karthikeyan [5 ,6 ,7 ]
机构
[1] Univ Yaounde I, Fac Sci, Lab Elect & Elect Syst, Yaounde, Cameroon
[2] Chennai Inst Technol, Ctr Artificial Intelligence, Chennai, India
[3] Univ Dschang, UR AIA, IUT FV Bandjoun, Dschang, Cameroon
[4] Univ Yaounde I, Fac Sci, Lab Mech, Yaounde, Cameroon
[5] Chennai Inst Technol, Ctr Nonlinear Syst, Chennai, India
[6] Chandigarh Univ, Dept Elect & Commun Engn, Mohali 10413, Punjab, India
[7] Chandigarh Univ, Univ Ctr Res & Dev, Mohali 10413, Punjab, India
来源
关键词
Coupled oscillators; bifurcation analysis; coexisting dynamics; basins of attraction; PSpice circuit simulation; PREDICTOR-CORRECTOR APPROACH; TRANSIENT CHAOS; DYNAMICAL ANALYSIS; CIRCUIT; ANTIMONOTONICITY; IMPLEMENTATION; MEMRISTOR; BEHAVIOR;
D O I
10.1142/S0218127423300045
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Undoubtedly, multistability represents one of the most followed venues for researchers working in the field of nonlinear science. Multistability refers to the situation where a combination of two or more attractors occurs for the same rank of parameters. However, to the best of our knowledge, the situation encountered in the relevant literature is never one where periodicity, chaos and hyperchaos coexist. In this article, we study a fourth-order autonomous dynamical system composing of a Duffing oscillator coupled to a van der Pol oscillator. Coupling consists in disturbing the amplitude of one oscillator with a signal proportional to the amplitude of the other. We exploit analytical and numerical methods (bifurcation diagrams, phase portraits, basins of attraction) to shed light on the plethora of bifurcation modes exhibited by the coupled system. Several ranks of parameters are revealed where the coupled system exhibits two or more competing behaviors. In addition to the transient dynamics, the most gratifying behavior reported in this article concerns the coexistence of four attractors consisting of a limit cycle of period-n, a pair of chaotic attractors and a hyperchaotic attractor. The impact of a fractional-order derivative is also examined. A physical implementation of the coupled oscillator system is performed and the PSpice simulations confirm the predictions of the theoretical study conducted in this work.
引用
收藏
页数:31
相关论文
共 50 条
  • [31] 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)
  • [32] Strongly resonant bifurcations of nonlinearly coupled Van der Pol-Duffing Oscillator
    Gan, CB
    Lu, QS
    Huang, KL
    APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1999, 20 (01) : 68 - 75
  • [33] Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator
    Wei, X.
    Randrianandrasana, M. F.
    Ward, M.
    Lowe, D.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2011, 2011
  • [34] A van der Pol-Duffing Oscillator with Indefinite Degree
    Hebai Chen
    Jie Jin
    Zhaoxia Wang
    Baodong Zhang
    Qualitative Theory of Dynamical Systems, 2022, 21
  • [35] On bifurcations and chaos in the Van der Pol-Duffing oscillator
    Bykov, VV
    RADIOTEKHNIKA I ELEKTRONIKA, 1997, 42 (09): : 1084 - 1096
  • [36] Strongly resonant bifurcations of nonlinearly coupled van der pol-duffing oscillator
    Chunbiao G.
    Qishao L.
    Kelei H.
    Applied Mathematics and Mechanics, 1999, 20 (1) : 68 - 75
  • [37] Synchronization of van der Pol oscillator and Chen chaotic dynamical system
    Elabbasy, E. M.
    EI-Dessoky, M. M.
    CHAOS SOLITONS & FRACTALS, 2008, 36 (05) : 1425 - 1435
  • [38] Effect of bounded noise on the chaotic motion of a Duffing Van der Pol oscillator in a φ6 potential
    Yang, XL
    Xu, W
    Sun, ZK
    CHAOS SOLITONS & FRACTALS, 2006, 27 (03) : 778 - 788
  • [39] Adaptive backstepping control and synchronization of a modified and chaotic Van der Pol-Duffing oscillator
    Vincent U.E.
    Odunaike R.K.
    Laoye J.A.
    Gbindinninuola A.A.
    Journal of Control Theory and Applications, 2011, 9 (2): : 273 - 277
  • [40] Period-doubling Cascades and Strange Attractors in Extended Duffing-Van der Pol Oscillator
    Yu Jun
    Pan Wei-Zhen
    Zhang Rong-Bo
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2009, 51 (05) : 865 - 868