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

DOI10.1007/s40863-023-00368-6OpenAlexW4381280720WikidataQ125423672 ScholiaQ125423672MaRDI QIDQ6188403

Luis Fernando Mello, Fabio Scalco Dias, Denis de Carvalho Braga, Jaume Llibre

Publication date: 11 January 2024

Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40863-023-00368-6

zbMATH Keywords

limit cycleglobal asymptotic stabilitypiecewise differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Discontinuous ordinary differential equations (34A36) Global stability of solutions to ordinary differential equations (34D23)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The matching of two stable sewing linear systems in the plane
• A polynomial counterexample to the Markus-Yamabe conjecture
• Structurally stable discontinuous vector fields in the plane.
• A solution to the bidimensional global asymptotic stability conjecture
• Asymptotic stability of linearizations of a planar vector field with a singular point implies global stability
• A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
• Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones