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

被引：0
作者：
Xiaopeng Zhao
David G. Schaeffer
Carolyn M. Berger
Daniel J. Gauthier
机构：
[1] Duke University,Department of Biomedical Engineering Center for Nonlinear and Complex Systems
[2] Duke University,Department of Mathematics Center for Nonlinear and Complex Systems
[3] Duke University,Department of Physics and Center for Nonlinear and Complex Systems
来源：
Nonlinear Dynamics | 2007年 / 48卷
关键词：
Prebifurcation amplification; Period-doubling bifurcation; Cardiac dynamics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：381 / 389
页数：8
相关论文
共 39 条
[1]  
Heldstab J.(1983)Linear and nonlinear response of discrete dynamical systems I Periodic attractors. Z. Phys. B 50 141-150
[2]  
Thomas H.(1984)Scaling for a periodic forcing of a period-doubling system Phys. Rev. Lett. 53 86-642
[3]  
Geisel T.(1987)Transitions to chaos in the presence of an external periodic field – crossover effect in the measure of critical exponents Europhys. Lett. 3 643-545
[4]  
Randons G.(1984)Effect of a periodic external perturbation on a system which exhibits an order-chaos transition through period-doubling bifurcation JETP Lett. 39 133-undefined
[5]  
Arneodo A.(1989)Renormalization group for the response function and spectrum of the period-doubling system Phys. Lett. A 94 1-undefined
[6]  
Argoul F.(2000)Different types of scaling in the dynamics of period-doubling maps under external periodic driving Discrete Dyn. Nat. Soc. 5 223-undefined
[7]  
Arneodo A.(1985)Virtual Hopf phenomenon: a new precursor of period-doubling bifurcations Phys. Rev. A 32 1744-undefined
[8]  
Richetti O.(1986)Small-signal amplification in bifurcating dynamical systems Phys. Rev. A 33 629-undefined
[9]  
Roux J.C.(1986)Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems Phys. Rev. A 33 2525-undefined
[10]  
Swinney H.L.(1992)Scaling law for the idler near a bifurcation Phys. Rev. A 46 787-undefined
1234