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Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators

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  • Sabarathinam, S.
  • Thamilmaran, K.

Abstract

In this work, transient chaos in a ring and globally coupled system of nearly conservative Hamiltonian Duffing oscillators is reported. The networks are formed by coupling of three, four and six Duffing oscillators. The nearly conservative Hamiltonian nature of the coupled system is proved by stability analysis. The transient phenomenon is confirmed through various numerical investigations such as recurrence analysis, 0–1 test and Finite Time Lyapunov Exponents. Further, the effect of damping and the average transient lifetime of three, four and six coupled schemes for randomly generated initial conditions have been analyzed. The experimental confirmation of transient chaos in an illustrative system of three ringly coupled Duffing oscillators is also presented.

Suggested Citation

  • Sabarathinam, S. & Thamilmaran, K., 2015. "Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 129-140.
    • Handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:129-140
    DOI: 10.1016/j.chaos.2015.01.004
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    Cited by:

    1. Wang, Zheng & Luo, Tianqi, 2017. "Multiformity of periodic-impact motions of a harmonically forced soft-impacting system and experimental verification based on an electronic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 23-36.
    2. Yan, Dengwei & Wang, Lidan & Duan, Shukai & Chen, Jiaojiao & Chen, Jiahao, 2021. "Chaotic Attractors Generated by a Memristor-Based Chaotic System and Julia Fractal," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Ngamsa Tegnitsap, J.V. & Fotsin, H.B., 2022. "Multistability, transient chaos and hyperchaos, synchronization, and chimera states in wireless magnetically coupled VDPCL oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Margielewicz, Jerzy & Gąska, Damian & Haniszewski, Tomasz & Litak, Grzegorz & Wolszczak, Piotr & Borowiec, Marek & Sosna, Petr & Ševeček, Oldřich & Rubeš, Ondřej & Hadaš, Zdeněk, 2024. "Vibration energy harvesting system with cyclically time-varying potential barrier," Applied Energy, Elsevier, vol. 367(C).
    5. Lazare Osmanov & Ramaz Khomeriki, 2022. "Regular and chaotic motion of two bodies swinging on a rod," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-7, November.
    6. Ling Zhou & Zhenzhen You & Xiaolin Liang & Xiaowu Li, 2022. "A Memristor-Based Colpitts Oscillator Circuit," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    7. Balaraman, Sundarambal & Kengne, Jacques & Kamga Fogue, M.S. & Rajagopal, Karthikeyan, 2023. "From coexisting attractors to multi-spiral chaos in a ring of three coupled excitation-free Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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