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Article
Small-signal Amplification of Period-doubling Bifurcations in Smooth Iterated Maps
Nonlinear Dynamics (2007)
  • Xiaopeng Zhao, University of Tennessee, Knoxville
  • David G. Schaeffer, Duke University
  • Carolyn M. Berger, Duke University
  • Daniel J. Gauthier, Duke University
Abstract

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.

Keywords
  • Prebifurcation amplification,
  • Period-doubling bifurcation,
  • Cardiac dynamics
Publication Date
June, 2007
Citation Information
Xiaopeng Zhao, David G. Schaeffer, Carolyn M. Berger and Daniel J. Gauthier. "Small-signal Amplification of Period-doubling Bifurcations in Smooth Iterated Maps" Nonlinear Dynamics Vol. 48 Iss. 4 (2007)
Available at: http://works.bepress.com/xiaopeng_zhao/4/