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 Citations (Scopus)

86 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)	2242-2261
Number of pages	20
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

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Publisher Copyright:
© 2024 Society for Industrial and Applied Mathematics.

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

singularities
piecewise smooth systems
classification

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10.1137/23M1622842

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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

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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.",

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AU - Homer, Martin E

AU - Jeffrey, Mike R

AU - Szalai, Robert

PY - 2024/9/1

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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)

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EP - 2261

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

Bibliographical note

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Keywords

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