Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps
| Autor: | Xiaopeng Zhao, Daniel J. Gauthier, David G. Schaeffer, Carolyn M. Berger |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2006 |
| Předmět: |
Period-doubling bifurcation
Applied Mathematics Mechanical Engineering Mathematical analysis FOS: Physical sciences Aerospace Engineering Perturbation (astronomy) Ocean Engineering Linear analysis Nonlinear Sciences - Chaotic Dynamics 01 natural sciences Article 010305 fluids & plasmas Amplitude Control and Systems Engineering Iterated function Control theory 0103 physical sciences Chaotic Dynamics (nlin.CD) Electrical and Electronic Engineering 010306 general physics Signal amplification Bifurcation Mathematics |
| Popis: | 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 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. 12 pages, 7 figures |
| Databáze: | OpenAIRE |
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