Nonlinear Dynamics

, Volume 48, Issue 4, pp 381–389

Small-signal amplification of period-doubling bifurcations in smooth iterated maps

  • Xiaopeng Zhao
  • David G. Schaeffer
  • Carolyn M. Berger
  • Daniel J. Gauthier
Original Article

DOI: 10.1007/s11071-006-9092-2

Cite this article as:
Zhao, X., Schaeffer, D.G., Berger, C.M. et al. Nonlinear Dyn (2007) 48: 381. doi:10.1007/s11071-006-9092-2

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 amplificationPeriod-doubling bifurcationCardiac dynamics

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Xiaopeng Zhao
    • 1
  • David G. Schaeffer
    • 2
  • Carolyn M. Berger
    • 3
  • Daniel J. Gauthier
    • 1
    • 3
  1. 1.Department of Biomedical Engineering Center for Nonlinear and Complex SystemsDuke UniversityDurhamUSA
  2. 2.Department of Mathematics Center for Nonlinear and Complex SystemsDuke UniversityDurhamUSA
  3. 3.Department of Physics and Center for Nonlinear and Complex SystemsDuke UniversityDurhamUSA