The discontinuous matching of two globally asymptotically stable crossing piecewise smooth systems in the plane do not produce in general a piecewise differential system globally asymptotically stable
de Carvalho Braga, Denis (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
Dias, Fabio Scalco (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mello, Luis Fernando (Universidade Federal de Itajubá. Instituto de Matemática e Computação)

Date:	2023
Abstract:	A differential system in the plane R2 is globally asymptotically stable if it has an equilibrium point p and all the other orbits of the system tend to p in forward time. In other words if the basin of attraction of p is R2. The problem of determining the basin of attraction of an equilibrium point is one of the main problems in the qualitative theory of differential equations. We prove that planar crossing piecewise smooth systems with two zones formed by two globally asymptotically stable differential systems sharing the same equilibrium point localized in the separation line are not necessarily globally asymptotically stable.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Piecewise differential system ; Global asymptotic stability ; Limit cycle
Published in:	São Paulo Journal of Mathematical Sciences, Vol. 17, Issue 2 (December 2023) , p. 671-678, ISSN 2316-9028

DOI: 10.1007/s40863-023-00368-6

Postprint 7 p, 690.7 KB

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