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Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback

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  • Sun, Zhongkui
  • Xu, Wei
  • Yang, Xiaoli
  • Fang, Tong

Abstract

The chaotic behavior of a double-well Duffing oscillator with both delayed displacement and velocity feedbacks under a harmonic excitation is investigated. By means of the Melnikov technique, necessary condition for onset of chaos resulting from homoclinic bifurcation is derived analytically. The analytical results reveal that for negative feedback the presence of time delay lowers the threshold and enlarges the possible chaotic domain in parameter space; while for positive feedback the presence of time delay enhances the threshold and reduces the possible chaotic domain in parameter space, which are further verified numerically through Poincare maps of the original system. Furthermore, the effect of the control gain parameters on the chaotic motion of the original system is studied in detail.

Suggested Citation

  • Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2006. "Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 705-714.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:3:p:705-714
    DOI: 10.1016/j.chaos.2005.04.041
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    Cited by:

    1. Huang, Dongmei & Li, Wei & Yang, Guidong & He, Meijuan, 2018. "Analysis of limit cycles and stochastic responses of a real-power vibration isolation system under delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 125-134.
    2. Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2007. "Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 39-53.
    3. Qin Guo & Zhongkui Sun & Ying Zhang & Wei Xu, 2019. "Time-Delayed Feedback Control in the Multiple Attractors Wind-Induced Vibration Energy Harvesting System," Complexity, Hindawi, vol. 2019, pages 1-11, January.
    4. Chu, Yan-Dong & Li, Xian-Feng & Zhang, Jian-Gang & Chang, Ying-Xiang, 2009. "Nonlinear dynamics analysis of a modified optically injected semiconductor lasers model," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 14-27.
    5. Naik, Raghavendra D. & Singru, Pravin M., 2012. "Stability and Hopf bifurcation of a Nonlinear oscillator with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1387-1396.
    6. Guo, Qin & Sun, Zhongkui & Xu, Wei, 2019. "Delay-induced transitions in the birhythmic biological model under joint noise sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 337-348.
    7. Zhou, Biliu & Jin, Yanfei & Xu, Huidong, 2022. "Global dynamics for a class of tristable system with negative stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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