Smallsignal amplification of perioddoubling bifurcations in smooth iterated maps
 Xiaopeng Zhao,
 David G. Schaeffer,
 Carolyn M. Berger,
 Daniel J. Gauthier
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Various authors have shown that, near the onset of a perioddoubling 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.
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 Title
 Smallsignal amplification of perioddoubling bifurcations in smooth iterated maps
 Journal

Nonlinear Dynamics
Volume 48, Issue 4 , pp 381389
 Cover Date
 20070601
 DOI
 10.1007/s1107100690922
 Print ISSN
 0924090X
 Online ISSN
 1573269X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Prebifurcation amplification
 Perioddoubling bifurcation
 Cardiac dynamics
 Industry Sectors
 Authors

 Xiaopeng Zhao ^{(1)}
 David G. Schaeffer ^{(2)}
 Carolyn M. Berger ^{(3)}
 Daniel J. Gauthier ^{(1)} ^{(3)}
 Author Affiliations

 1. Department of Biomedical Engineering Center for Nonlinear and Complex Systems, Duke University, Durham, NC, 27708, USA
 2. Department of Mathematics Center for Nonlinear and Complex Systems, Duke University, Durham, NC, 27708, USA
 3. Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, NC, 27708, USA