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A Smooth and Discontinuous OscillatorWada Basin Dynamics

A Smooth and Discontinuous Oscillator: Wada Basin Dynamics [This chapter investigates a specific point of the very intricate asymptotic behaviourAsymptotic behaviour of the SD oscillatorSD oscillator, which is known as the Wada basin dynamics. The oscillator is subjected to a linear viscous damping and to a sinusoidal forcing. As described and already observed through direct numerical integration, this system may possess more than twenty coexisted low-period periodic attractorsLow-period periodic attractor for a given set of parameters. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction. We obtain the so-called Wada basins of which the boundaries are rigorously described.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Smooth and Discontinuous OscillatorWada Basin Dynamics

Part of the Springer Tracts in Mechanical Engineering Book Series
Cao, Qingjie; Léger, Alain
Springer Journals — Sep 28, 2016
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21 pages

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2017
ISBN
978-3-662-53092-4
Pages
67 –88
DOI
10.1007/978-3-662-53094-8_6
Publisher site
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Abstract

[This chapter investigates a specific point of the very intricate asymptotic behaviourAsymptotic behaviour of the SD oscillatorSD oscillator, which is known as the Wada basin dynamics. The oscillator is subjected to a linear viscous damping and to a sinusoidal forcing. As described and already observed through direct numerical integration, this system may possess more than twenty coexisted low-period periodic attractorsLow-period periodic attractor for a given set of parameters. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction. We obtain the so-called Wada basins of which the boundaries are rigorously described.]

Published: Sep 28, 2016

Keywords: Periodic Point; Unstable Manifold; Stable Manifold; Basin Boundary; Periodic Attractor

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