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Devil’s staircases in a thermoacoustic system with sinusoidal excitations

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Abstract

The influences of sinusoidal excitations on a Rijke tube system through the introduction of nonlinear dynamics are investigated in detail. The system is governed by one-dimensional partial differential equations, which are addressed by means of the Galerkin procedure and analysed from the viewpoint of nonlinear dynamics. The results show a rich variety of behaviours in the system, including subcritical bifurcation, hysteresis and phase locking. In certain parameter ranges, the solution switches between periodic and quasi-periodic. These ranges mainly depend on the intensity of the heat source in the tube. The phase-locking intervals that correspond to periodic solutions compose a devil’s staircase, whose Lebesgue measure increases as the amplitude of the excitation increases.

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Authors and Affiliations

  1. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Zhengyuan Zhang, Jiazhong Zhang, Pengyu Fan & Yongsen He

Authors
  1. Zhengyuan Zhang
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  2. Jiazhong Zhang
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  3. Pengyu Fan
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  4. Yongsen He
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Correspondence to Jiazhong Zhang.

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Zhang, Z., Zhang, J., Fan, P. et al. Devil’s staircases in a thermoacoustic system with sinusoidal excitations. Eur. Phys. J. Spec. Top. 228, 1891–1901 (2019). https://doi.org/10.1140/epjst/e2019-800226-7

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  • DOI: https://doi.org/10.1140/epjst/e2019-800226-7

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