Corner collision implies border-collision bifurcation
نویسندگان
چکیده
منابع مشابه
Border Collision bifurcation Control of Cardiac Alternans
The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period doubling border collision ...
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In this work we study some properties associated with the bordercollision bifurcations in a two-dimensional piecewise linear map in canonical form, related to the case in which a xed point of one of the linear maps has complex eigenvalues and undergoes a center bifurcation when its eigenvalues pass through the unit circle. This problem is faced in several applied piecewise smooth models, such ...
متن کاملCardiac Alternans Arising from an Unfolded Border-Collision Bifurcation
Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a perioddoubling bifurcation, where the resulting alternation of the ac...
متن کاملDangerous bifurcation at border collision: when does it occur?
It has been shown recently that border collision bifurcation in a piecewise smooth map can lead to a situation where a fixed point remains stable at both sides of the bifurcation point, and yet the orbit becomes unbounded at the point of bifurcation because the basin of attraction of the stable fixed point shrinks to zero size. Such bifurcations have been named "dangerous bifurcations." In this...
متن کاملBorder-collision bifurcations: An explanation for observed bifurcation phenomena.
Recently physical and computer experiments involving systems describable by continuous maps that are nondi8'erentiable on some surface in phase space have revealed novel bifurcation phenomena. These phenomena are part of a rich new class of bifurcations which we call border collisi-on bifurcations A. general criterion for the occurrence of border-collision bifurcations is given. Illustrative nu...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2001
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(01)00250-0