Simultaneous Border-Collision and Period-Doubling Bifurcations

Details Simultaneous Border-Collision and Period-Doubling Bifurcations Simultaneous Border-Collision and Period-Doubling Bifurcations

2009-05-22

arxiv.org/abs/0905.3730v1

Mathematics

Dynamical Systems

22 pages; 5 figures

Scientific paper

We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely classified; in particular, we give conditions that ensure chaos.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-326027