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首页> 外文期刊>Mathematical Problems in Engineering >Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator
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Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol Oscillator

机译：耦合到Van der Pol振荡器的周期性驱动Duffing谐振器的非线性动力学

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摘要

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1:1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.
机译：我们探讨了在弱耦合和强耦合的情况下，在内部共振为1：1的情况下，弹性耦合到范德波尔振荡器的周期性驱动Duffing共振器的动力学。强耦合导致主导同步，而弱耦合情况则导致众多复杂行为。使用二次标度方法来获得频率-幅度调制。内部共振导致Duffing共振器的反共振响应和van der Pol振荡器的停滞响应（曲线上的小肩部）。还分析了动态运动的稳定性。耦合系统显示出滞后响应模式和破坏对称性的方面。还观察到耦合系统的混沌行为，并使用分叉分析研究了系统动力学对参数的依赖性。

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第speca期|p.248328.1-248328.16|共16页
  • 作者

    X. Wei; M. F. Randrianandrasana; M. Ward; D. Lowe;

  • 作者单位

    School of Mechanical Engineering, University of Birmingham, Birmingham B4 7ET, UK;

    Nonlinearity and Complexity Research Group, Aston University, Birmingham B15 2TT, UK;

    School of Mechanical Engineering, University of Birmingham, Birmingham B4 7ET, UK;

    Nonlinearity and Complexity Research Group, Aston University, Birmingham B15 2TT, UK;

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