Resonance near border-collision bifurcations in piecewise-smooth, continuous maps
نویسندگان
چکیده
منابع مشابه
Border collision bifurcations in two-dimensional piecewise smooth maps
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle-node, pitchfork, or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and clas...
متن کاملFeedback Control of Border Collision Bifurcations in Piecewise Smooth Systems
Feedback controls that stabilize border collision bifurcations are designed for piecewise smooth systems undergoing border collision bifurcations. The paper begins with a summary of the main results on border collision bifurcations, and proceeds to a study of stabilization of these bifurcations for one-dimensional systems using both static and dynamic feedback. The feedback can be applied on on...
متن کاملBorder Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps
Abstract. In this paper we report some important results that help in analizing the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the plane of discontinuity. Earlier, Feigin had made a similar analysis for general n-dimensional piecewise smooth continuous maps. Proceeding along sim...
متن کاملCodimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps
We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequen...
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Abstract. We show that maps describing border collision bifurcations (continuous but non-differentiable discrete time maps) are subject to a curse of dimensionality: it is impossible to reduce the study of the general case to low dimensions, since in every dimension the bifurcation can produce fundamentally different attractors (contrary to the case of local bifurcations in smooth systems). In ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2010
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/23/12/006