Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems

Paul Glendinning; S J Hogan; Martin E Homer; Mike R Jeffrey; Robert Szalai

doi:10.1137/23M1622842

Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems

Paul Glendinning, S J Hogan^*, Martin E Homer, Mike R Jeffrey, Robert Szalai

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Downloads (Pure)

Abstract

We classify Filippov's type 3 singular points of planar bimodal piecewise smooth systems. These singular points consist of fold or cusp tangencies of the vector fields to both sides of a switching surface. For isolated analytic type 3 singular points there are 25 topological classes, up to time reversal. For isolated general type 3 singular points there are 40 topological classes, up to time reversal.

Original language	English
Pages (from-to)	2242
Number of pages	2261
Journal	SIAM Journal on Applied Dynamical Systems
Volume	23
Issue number	3
Early online date	20 Aug 2024
DOIs	https://doi.org/10.1137/23M1622842
Publication status	Published - 1 Sept 2024

Keywords

singularities
piecewise smooth systems
classification

Access to Document

10.1137/23M1622842

Full-text PDF (accepted manuscript)
This is the accepted author manuscript (AAM) of the article which has been made Open Access under the University of Bristol's Scholarly Works Policy. The final published version (Version of Record) can be found on the publisher's website. The copyright of any third-party content, such as images, remains with the copyright holder.
Accepted author manuscript, 565 KBLicence: CC BY

Handle.net

Persistent link

Cite this

@article{4139b3868d7444d99047b0b84078ff04,

title = "Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems",

abstract = "We classify Filippov's type 3 singular points of planar bimodal piecewise smooth systems. These singular points consist of fold or cusp tangencies of the vector fields to both sides of a switching surface. For isolated analytic type 3 singular points there are 25 topological classes, up to time reversal. For isolated general type 3 singular points there are 40 topological classes, up to time reversal.",

keywords = "singularities, piecewise smooth systems, classification",

author = "Paul Glendinning and Hogan, {S J} and Homer, {Martin E} and Jeffrey, {Mike R} and Robert Szalai",

year = "2024",

month = sep,

day = "1",

doi = "10.1137/23M1622842",

language = "English",

volume = "23",

pages = "2242",

journal = "SIAM Journal on Applied Dynamical Systems",

issn = "1536-0040",

publisher = "Society of Industrial and Applied Mathematics",

number = "3",

}

TY - JOUR

T1 - Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems

AU - Glendinning, Paul

AU - Hogan, S J

AU - Homer, Martin E

AU - Jeffrey, Mike R

AU - Szalai, Robert

PY - 2024/9/1

Y1 - 2024/9/1

N2 - We classify Filippov's type 3 singular points of planar bimodal piecewise smooth systems. These singular points consist of fold or cusp tangencies of the vector fields to both sides of a switching surface. For isolated analytic type 3 singular points there are 25 topological classes, up to time reversal. For isolated general type 3 singular points there are 40 topological classes, up to time reversal.

AB - We classify Filippov's type 3 singular points of planar bimodal piecewise smooth systems. These singular points consist of fold or cusp tangencies of the vector fields to both sides of a switching surface. For isolated analytic type 3 singular points there are 25 topological classes, up to time reversal. For isolated general type 3 singular points there are 40 topological classes, up to time reversal.

KW - singularities

KW - piecewise smooth systems

KW - classification

U2 - 10.1137/23M1622842

DO - 10.1137/23M1622842

M3 - Article (Academic Journal)

SN - 1536-0040

VL - 23

SP - 2242

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

IS - 3

ER -

Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this