DocumentCode
1442571
Title
Formation of a fractal basin boundary in a forced oscillator
Author
Dobson, Ian
Author_Institution
Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA
Volume
36
Issue
6
fYear
1989
fDate
6/1/1989 12:00:00 AM
Firstpage
866
Lastpage
872
Abstract
The question of how a fractal basin boundary arises in the sinusoidally forced Duffing´s equation is considered. The author describes how the backwards system flow deforms a local stable manifold into the fractal boundary. Parts of the boundary are labeled in a way related to their time of formation. The truncated fractal boundary produced by a burst of sinusoidal forcing is briefly considered. The approach supplements the insights provided by the usual Poincare map techniques
Keywords
fractals; nonlinear network analysis; oscillators; stability; backwards system flow; forced oscillator; fractal basin boundary; local stable manifold; sinusoidally forced Duffing´s equation; Circuits and systems; Equations; Footwear; Fractals; H infinity control; Orbits; Oscillators; Systems engineering and theory;
fLanguage
English
Journal_Title
Circuits and Systems, IEEE Transactions on
Publisher
ieee
ISSN
0098-4094
Type
jour
DOI
10.1109/31.90406
Filename
90406
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