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Existence and stability of periodic oscillations of a smooth and discontinuous oscillator

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  • Liang, Zaitao
  • Yang, Yanjuan

Abstract

In this paper, we study the existence, multiplicity and Lyapunov stability of periodic oscillations of a SD oscillator which exhibits both discontinuous and smooth dynamics depending on the value of the smoothness parameter α. Both linear stability and nonlinear stability results are obtained. The proof is based on some stability criteria of second order differential equations combined with the quantitative information obtained by the method of upper and lower solutions. Moreover, some numerical simulations are provided to illustrate the results.

Suggested Citation

  • Liang, Zaitao & Yang, Yanjuan, 2020. "Existence and stability of periodic oscillations of a smooth and discontinuous oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120302284
    DOI: 10.1016/j.physa.2020.124511
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    References listed on IDEAS

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    1. Yang, Tao & Liu, Jiye & Cao, Qingjie, 2018. "Response analysis of the archetypal smooth and discontinuous oscillator for vibration energy harvesting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 358-373.
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