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


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Zhao, X; Schaeffer, DG; Berger, CM; Gauthier, DJ

Published Date

  • June 2007

Published In

Volume / Issue

  • 48 / 4

Start / End Page

  • 381 - 389

PubMed ID

  • 19112525

Pubmed Central ID

  • 19112525

International Standard Serial Number (ISSN)

  • 0924-090X

Digital Object Identifier (DOI)

  • 10.1007/s11071-006-9092-2


  • eng