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.Comment: 12 pages, 7 figure
