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Study on fractional-order coupling of high-order Duffing oscillator and its application

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  • Li, Guohui
  • Xie, Ruiting
  • Yang, Hong

Abstract

Inspired by the existing Duffing oscillator, a high-order Duffing oscillator (HODO) is proposed, its fractional-order coupled chaotic oscillator is studied by introducing a high-order nonlinear restoring force term. First, the bifurcation point of the HODO is analyzed through the bifurcation diagram, and the critical threshold of the system is determined based on the phase trajectory, and applied to the amplitude detection. Use Simulink to model HODO to display different phase trajectories. Secondly, the fractional-order high-order Duffing oscillator (FOHODO) is studied, and the results exhibit its nonlinear characteristics that differ from HODO. Then, the critical state of the fractional-order high-order Duffing coupled Van der Pol oscillator (FOHOD-VPO) is studied, and it is successfully applied to detect the multi-line spectrum periodic signals and ship-radiated noise (S-RN). Finally, in the performance analysis, the input signal-to-noise ratio (SNR) threshold of the HODO is lower, which is −33.47 dB. The performance of the FOHOD-VPO considering the coupling factor and fractional derivative is better than that of the HODO. The input SNR threshold of the FOHOD-VPO is −70.97 dB. Research on high-order chaotic system is significantly better than traditional system in terms of anti-noise performance. Studying the essential characteristics of high-order chaotic system can be better applied to practical research.

Suggested Citation

  • Li, Guohui & Xie, Ruiting & Yang, Hong, 2024. "Study on fractional-order coupling of high-order Duffing oscillator and its application," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008075
    DOI: 10.1016/j.chaos.2024.115255
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    References listed on IDEAS

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    1. He, Yuzhu & Fu, Yuxuan & Qiao, Zijian & Kang, Yanmei, 2021. "Chaotic resonance in a fractional-order oscillator system with application to mechanical fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Min Chai & Lei Ba, 2021. "Application of EEG Signal Recognition Method Based on Duffing Equation in Psychological Stress Analysis," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-10, September.
    3. Giresse, Tene Alain & Crépin, Kofane Timoleon, 2017. "Chaos generalized synchronization of coupled Mathieu-Van der Pol and coupled Duffing-Van der Pol systems using fractional order-derivative," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 88-100.
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