Title :
Formation of a fractal basin boundary in a forced oscillator
Author_Institution :
Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA
fDate :
6/1/1989 12:00:00 AM
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;
Journal_Title :
Circuits and Systems, IEEE Transactions on
