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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
Published on: February 3, 2014
Border collision bifurcation of a resonant closed invariant curve
Zh T Zhusubaliyev1, V Avrutin2, I Sushko3
1Department of Computer Science, Dynamics of Non-Smooth Systems International Scientific Laboratory, Southwest State University, 50 Years of October St. 94, 305040 Kursk, Russia.
Abstract:
This paper contributes to studying the bifurcations of closed invariant curves in piecewise-smooth maps. Specifically, we discuss a border collision bifurcation of a repelling resonant closed invariant curve (a repelling saddle-node connection) colliding with the border by a point of the repelling cycle. As a result, this cycle becomes attracting and the curve is destroyed, while a new repelling closed invariant curve appears (not in a neighborhood of the previously existing invariant curve), being associated with quasiperiodic dynamics. This leads to a global restructuring of the phase portrait since both curves mentioned above belong to basin boundaries of coexisting attractors.
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