Quasiperiodically forced dynamical systems with strange nonchaotic attractors

We discuss the existence and properties of strange nonchaotic attractors of quasiperiodically forced nonlinear dynamical systems. We do this by examining a particular model differential equation, φ ̇ = cos φ + ε cos 2φ + ⨍(t) , where ⨍ is a two-frequency quasiperiodic function of t. When ϵ = 0 the a...

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Bibliographic Details
Published in:Physica. D 1987, Vol.26 (1), p.277-294
Main Authors: Romeiras, Filipe J., Bondeson, Anders, Ott, Edward, Antonsen, Thomas M., Grebogi, Celso
Format: Article
Language:English
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Summary:We discuss the existence and properties of strange nonchaotic attractors of quasiperiodically forced nonlinear dynamical systems. We do this by examining a particular model differential equation, φ ̇ = cos φ + ε cos 2φ + ⨍(t) , where ⨍ is a two-frequency quasiperiodic function of t. When ϵ = 0 the analysis of the equation is facilitated since then it can be related to the Schrödinger equation with quasiperiodic potential. We show that the equation does indeed exhibit strange nonchaotic attractors, and we consider the important question of whether these attractors are typical in the sense that they exist on a set of positive Lebesgue measure in parameter space. (The equation also exhibits two- and three-frequency quasiperiodic behavior.) We also show that the strange nonchaotic attractors have distinctive frequency spectrum; this property might make them experimentally observable.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(87)90229-6