Abstract
A semianalytical method is derived for finding the existence and stability of single-impact periodicorbits born in a boundary equilibrium bifurcation in a generaln-dimensional impacting hybridsystem. Known results are reproduced for planar systems and general formulae derived for three-dimensional (3D) systems. A numerical implementation of the method is illustrated for several 3Dexamples and for an 8D wing-flap model that shows coexistence of attractors. It is shown how themethod can easily be embedded within numerical continuation, and some remarks are made aboutnecessary and sufficient conditions in arbitrary dimensional systems
Original language | English |
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Article number | 4 |
Pages (from-to) | 3320 - 3357 |
Number of pages | 38 |
Journal | SIAM Journal on Applied Dynamical Systems |
Volume | 22 |
Issue number | 4 |
DOIs | |
Publication status | Published - 6 Dec 2023 |
Bibliographical note
Funding Information:\ast Received by the editors February 8, 2023; accepted for publication (in revised form) by V. Kirk July 28, 2023; published electronically December 6, 2023. https://doi.org/10.1137/23M1552292 Funding: The work of the first author was supported by the University of Bristol and Chinese Scholarship Council joint studentship 202006120007. \dagger Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK ([email protected], [email protected]).
Publisher Copyright:
© 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.
Research Groups and Themes
- Engineering Mathematics Research Group
Keywords
- impact
- hybrid system
- periodic orbit
- boundary equilibrium bifurcation