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Stability of a Spring-Mass System with Generalized Piecewise Constant Argument

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Progress on Difference Equations and Discrete Dynamical Systems (ICDEA 2019)

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Abstract

In this paper, we address a damped spring-mass system and develop it with piecewise constant argument of generalized type (PCAG). We investigate existence and uniqueness of the solutions of the proposed mechanical system. Then, we give sufficient conditions guaranteeing the uniform asymptotic stability of the trivial solution. While doing the stability examination, we use Lyapunov-Razumikhin method developed by Akhmet and Aruğaslan (Discrete and continuous dynamical systems. Series A, vol 25(2), pp 457–466, 2009, [1]) for differential equations with PCAG (EPCAG). Additionally, we present several examples with simulations.

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Acknowledgements

This work is supported by TÜBİTAK (The Scientific and Technological Research Council of Turkey) under project no 118F185 and supported partially by TÜBİTAK under project no 118F161. The authors want to express their sincere gratitude to the referee for the valuable remarks that improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Süleyman Demirel University, 32260, Isparta, Turkey

    DUYGU ARUĞASLAN ÇINÇIN

  2. Graduate School of Natural and Applied Sciences, Süleyman Demirel University, 32260, Isparta, Turkey

    Nur Cengiz

Authors
  1. DUYGU ARUĞASLAN ÇINÇIN
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  2. Nur Cengiz
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Correspondence to DUYGU ARUĞASLAN ÇINÇIN .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Steve Baigent

  2. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

    Martin Bohner

  3. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

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ARUĞASLAN ÇINÇIN, D., Cengiz, N. (2020). Stability of a Spring-Mass System with Generalized Piecewise Constant Argument. In: Baigent, S., Bohner, M., Elaydi, S. (eds) Progress on Difference Equations and Discrete Dynamical Systems. ICDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-030-60107-2_9

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