How chaotic are strange non-chaotic attractors?
نویسندگان
چکیده
منابع مشابه
How chaotic are strange nonchaotic attractors?
We show that the classic examples of quasi-periodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general class...
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The occurrence of strange non-chaotic attractors (SNA) in quasiperiodically forced systems has attracted considerable interest over the last two decades, in particular since it provides a rich class of examples for the possibility of complicated dynamics in the absence of chaos. Their existence was discovered in the early 1980’s, independently by Herman [1] for quasiperiodic SL(2, R)-cocycles a...
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It is shown how chaotic systems with more than one strange attractor can be controlled. Issues in controlling multiple (coexisting) strange attractors are stabilizing a desired motion within one attractor as well as taking the system dynamics from one attractor to another. Realization of these control objectives is demonstrated using a numerical example, the Newton–Leipnik system. 2002 Elsevi...
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We propose a general mechanism by which strange non-chaotic attractors (SNA) can be created during the collision of invariant tori in quasiperiodically forced systems, and then describe rigorously how this mechanism is implemented in certain parameter families of quasiperiodically forced interval maps. In these families a stable and an unstable invariant circle undergo a saddle-node bifurcation...
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The theory of chaotic dynamical systems can be a tricky area of study for a non-expert to break into. Because the theory is relatively recent, the new student finds himself immersed in a subject with very few clear and intuitive definitions. This paper aims to carve out a small section of the theory of chaotic dynamical systems – that of attractors – and outline its fundamental concepts from a ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2006
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/19/9/001