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Engineering Applications of Dynamics of Chaos pp 225–277Cite as

The Approximate Analytical Methods in the Study of Transition to Chaotic Motion in Nonlinear Oscillators

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 319))

Abstract

The chapter presents an approximate approach to the study of transition to chaotic response in forced dissipative oscillators. We show that mathematical techniques and concepts of the approximate theory of nonlinear oscillations can be useful in constructing approximate criteria for chaos, i.e. in estimating system parameter critical values, the values for which chaos can be expected. The attention is focused on the strange phenomena which are related to the escape from a potential well. Four classical oscillators are studied in detail: two-well potential system under a) dynamic harmonic load, b) combined parametric and dynamic load; the single potential system with quadratic nonlinearity, and Duffing’s softening type oscillator. The approximate criteria for chaos (or escape) are obtained in the form of simple algebraic formulae. Computer simulations confirm that the theoretical results provide us with a good estimation of the system parameter critical values where the “strange phenomena” really occur.

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Author information

Authors and Affiliations

  1. Polish Academy of Science, Warsaw, Poland

    W. Szemplinska-Stupnicka

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  1. W. Szemplinska-Stupnicka
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Editors and Affiliations

  1. IPPT-PAN, Warsaw, Poland

    W. Szemplinska-Stupnicka

  2. Technical University Vienna, Austria

    H. Troger

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© 1991 Springer-Verlag Wien

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Szemplinska-Stupnicka, W. (1991). The Approximate Analytical Methods in the Study of Transition to Chaotic Motion in Nonlinear Oscillators. In: Szemplinska-Stupnicka, W., Troger, H. (eds) Engineering Applications of Dynamics of Chaos. International Centre for Mechanical Sciences, vol 319. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2610-3_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2610-3_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82328-6

  • Online ISBN: 978-3-7091-2610-3

  • eBook Packages: Springer Book Archive

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