Structural Stability of the Two-Fold Singularity

At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves toward the switching manifold from both sides...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on applied dynamical systems 2012-01, Vol.11 (4), p.1215-1230
Main Authors: Fernández-García, S., García, D. Angulo, Tost, G. Olivar, di Bernardo, M., Jeffrey, M. R.
Format: Article
Language:English
Subjects:
Computer engineering
Dynamical systems
Manifolds
Mathematical analysis
Phase transitions
Singularities
Sliding
Switches
Switching
Vectors (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves toward the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different actions: it winds around the singularity by crossing repeatedly through, and passes through the singularity by sliding along, the switching manifold. The case when the number of rotations around the singularity is infinite has been analyzed in detail. Here we study the case when the flow makes a finite, but previously unknown, number of rotations around the singularity between incidents of sliding. We show that the solution is remarkably simple: the maximum and minimum numbers of rotations made anywhere in the flow differ only by one and increase incrementally with a single parameter---the angular jump in the flow direction across the switching manifold at the singularity. [PUBLICATION ABSTRACT]
ISSN:1536-0040
1536-0040
DOI:10.1137/120869134