Alternate Pacing of Border-Collision Period-Doubling Bifurcations

Details Alternate Pacing of Border-Collision Period-Doubling Bifurcations Alternate Pacing of Border-Collision Period-Doubling Bifurcations

2006-09-04

arxiv.org/abs/math/0609106v2

Mathematics

Dynamical Systems

14 pages, 5 figures; added funding reference

Scientific paper

Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise $\mathcal{C}^{1}$ map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision period-doubling bifurcations. We apply a subharmonic perturbation to the bifurcation parameter, which is also known as alternate pacing, and we investigate the response under such pacing near the original bifurcation point. The resulting behavior is characterized quantitatively by a gain, which is the ratio of the response amplitude to the applied perturbation amplitude. The gain in a border-collision period-doubling bifurcation has a qualitatively different dependence on parameters from that of a classical period-doubling bifurcation. Perhaps surprisingly, the differences are more readily apparent if the gain is plotted vs. the perturbation amplitude (with the bifurcation parameter fixed) than if plotted vs. the bifurcation parameter (with the perturbation amplitude fixed). When this observation is exploited, the gain under alternate pacing provides a useful experimental tool to identify a border-collision period-doubling bifurcation.

Affiliated with

Also associated with

No associations

Rating

Alternate Pacing of Border-Collision Period-Doubling Bifurcations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Alternate Pacing of Border-Collision Period-Doubling Bifurcations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Alternate Pacing of Border-Collision Period-Doubling Bifurcations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727340