Melnikov functions of arbitrary order for piecewise smooth differential systems in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math> and applications

Chen, Xingwu; Li, Tao; Llibre, Jaume

doi:10.1016/j.jde.2022.01.019

Cited by 10 publications

(1 citation statement)

References 42 publications

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“…Concerning the Melnikov method, in the recent years several interesting extensions have been achieved by different authors. The articles [13][14][15][16][17][18][19][20][21][22][23][24][25][26] and the references therein (just to mention a few main recent contributions in this area of research), show the great deal of interest in this topic both from the theoretical and the applied point of view. Most of the achieved results are general enough to cover the case of piecewise smooth differential systems which present a manifold of discontinuity.…”

Section: Introductionmentioning

confidence: 99%

An Application of the Melnikov Method to a Piecewise Oscillator

Gjata

Zanolin

2023

Contemp. Math.

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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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