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

Zaitao Liang and Yanjuan Yang

Physica A: Statistical Mechanics and its Applications, 2020, vol. 555, issue C

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.

Keywords: SD oscillator; Periodic solutions; Lyapunov stability; Twist (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120302284

DOI: 10.1016/j.physa.2020.124511

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