An Application of the Melnikov Method to a Piecewise Oscillator

Authors

  • Oltiana Gjata Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy
  • Fabio Zanolin Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy https://orcid.org/0000-0001-9105-3084

DOI:

https://doi.org/10.37256/cm.4220232160

Keywords:

Duffing equation, homoclinic trajectory, non-smooth systems, chaotic dynamics, Melnikov method

Abstract

In this paper we present a new application of the Melnikov method to a class of periodically perturbed Duffing equations where the nonlinearity is non-smooth as otherwise required in the classical applications. Extensions of the Melnikov method to these situations is a topic with growing interests from the researchers in the past decade. Our model, motivated by the study of mechanical vibrations for systems with ''stops'', considers a case of a nonlinear equation with piecewise linear components. This allows us to provide a precise analytical representation of the homoclinic orbit for the associated autonomous planar system and thus obtain simply computable conditions for the zeros of the associated Melnikov function.

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Published

2023-04-21

How to Cite

1.
Gjata O, Zanolin F. An Application of the Melnikov Method to a Piecewise Oscillator. Contemp. Math. [Internet]. 2023 Apr. 21 [cited 2024 Mar. 4];4(2):249-6. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2160