Border-collision bifurcations including “period two to period three” for piecewise smooth systems

Content Provider	Semantic Scholar
Author	Nusse, Helena E. Yorke, James A.
Copyright Year	1992
Abstract	Abstract We examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter μ. In the simplest case there is a surface Γ in phase space along which the map has no derivative (or has two one-sided derivatives). Γ is the border of two regions in which the map is smooth. As the parameter μ is varied, a fixed point Eμ may collide with the border Γ, and we may assume that this collision occurs at μ = 0. A variety of bifurcations occur frequently in such situations, but never or almost never occur in smooth systems. In particular Eμ may cross the border and so will exist for μ 0 but it may be a saddle in one case, say μ 0. For μ 0 there may be a stable period 3 orbit which similarly shrinks to E0 as μ→0. Hence one observes the following stable periodic orbits: a stable period 2 orbit collapses to a point and is reborn as a stable period 3 orbit. We also see analogously “stable period 2 to stable period p orbit bifurcations”, with p = 5,11,52, or period 2 to quasi-periodic or even to a chaotic attractor. We believe this phenomenon will be seen in many applications.
Starting Page	39
Ending Page	57
Page Count	19
File Format	PDF HTM / HTML
DOI	10.1016/0167-2789(92)90087-4
Volume Number	57
Alternate Webpage(s)	http://yorke.umd.edu/Yorke_papers_most_cited_and_post2000/1992_02_Nusse_PhysicaD_Border_collision_bifurcations.pdf
Alternate Webpage(s)	https://doi.org/10.1016/0167-2789%2892%2990087-4
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article