Small-signal amplification of period-doubling bifurcations in smooth iterated maps
نویسندگان
چکیده
منابع مشابه
Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps.
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed ...
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We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation eq...
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The concept of self-similarity is central to the notion of a fractal, but the actual symmetry group that generates that self-similarity is rarely named, and it seems fractals are almost never studied according to their symmetries. Yet, in other branches of mathematics and physics, it is well understood that symmetry provides a powerful mechanism for understanding systems. In this paper, we iden...
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We study the critical behavior of period doubling in two coupled onedimensional maps with a single maximum of order z. In particurlar, the effect of the maximum-order z on the critical behavior associated with coupling is investigated by a renormalization method. There exist three fixed maps of the period-doubling renormalization operator. For a fixed map associated with the critical behavior a...
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ژورنال
عنوان ژورنال: Nonlinear Dynamics
سال: 2006
ISSN: 0924-090X,1573-269X
DOI: 10.1007/s11071-006-9092-2