Application of the subharmonic Melnikov method to piecewise-smooth systems

Kazuyuki Yagasaki

doi:10.3934/dcds.2013.33.2189

Article Contents

2013, Volume 33, Issue 5: 2189-2209. Doi: 10.3934/dcds.2013.33.2189

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Application of the subharmonic Melnikov method to piecewise-smooth systems

Kazuyuki Yagasaki^1,

1.
Mathematics Division, Department of Information Engineering, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181

Received: November 30, 2011

Revised: June 30, 2012

Published: April 2013

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Abstract

We extend a refined version of the subharmonic Melnikov method to piecewise-smooth systems and demonstrate the theory for bi- and trilinear oscillators. Fundamental results for approximating solutions of piecewise-smooth systems by those of smooth systems are given and used to obtain the main result. Special attention is paid to degenerate resonance behavior, and analytical results are illustrated by numerical ones.

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Mathematics Subject Classification: Primary: 37G15; Secondary: 34A36, 34E10.

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