Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps

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dc.creatorZhao, Xiaopeng
dc.creatorSchaeffer, David G.
dc.creatorBerger, Carolyn M.
dc.creatorGauthier, Daniel J.
dc.date2006-09-05
dc.date.accessioned2026-07-07T07:25:31Z
dc.date.available2026-07-07T07:25:31Z
dc.descriptionVarious 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 response is studied using normal forms based on the most general assumptions of iterated maps. Such an analysis provides a theoretical footing for previous experimental and numerical observations, such as the failure of linear analysis and the saturation of the gain. Qualitative as well as quantitative features of the gain are exhibited using selected models of cardiac dynamics.
dc.description12 pages, 7 figures
dc.identifierhttps://arxiv.org/abs/nlin/0609009
dc.identifierhttp://arxiv.org/abs/nlin/0609009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116742
dc.subjectChaotic Dynamics
dc.titleSmall-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps
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