The Dissipative Nonlocal Oscillator

The most important characteristics of a nonlocal and nonlinear oscillator subject to dissipative forces are extensively studied by means of an asymptotic perturbation method, based upon temporal rescaling and harmonic balance. The conditions under which bifurcations and limit cycles appear are deter...

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Bibliographic Details
Published inNonlinear dynamics Vol. 16; no. 4; pp. 307 - 320
Main Author Maccari, Attilio
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.08.1998
Subjects
Asymptotic methods
Bifurcations
Perturbation methods
Rescaling
Resonant frequencies
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ISSN0924-090X
1573-269X
DOI10.1023/A:1008290009964

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Summary:The most important characteristics of a nonlocal and nonlinear oscillator subject to dissipative forces are extensively studied by means of an asymptotic perturbation method, based upon temporal rescaling and harmonic balance. The conditions under which bifurcations and limit cycles appear are determined. If the parameters satisfy particular conditions, a quasi-periodic motion is predicted, because a second small frequency adds to the natural frequency of the oscillator. The analytical results are validated by numerically solving the original system.
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ISSN:0924-090X
1573-269X
DOI:10.1023/A:1008290009964