A singular approach to discontinuous vector fields on the plane

DOI10.1016/j.jde.2006.08.017zbMath1116.34008OpenAlexW2161389235MaRDI QIDQ858697

Claudio A. Buzzi, Paulo Ricardo da Silva, Marco Antonio Teixeira

Publication date: 11 January 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11449/34118

zbMATH Keywords

singular perturbationregularizationplanar systemgeometric singular perturbation theoryblowing upfast systemslow systemreduced problem

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Discontinuous ordinary differential equations (34A36) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chasse au canard
• Transversal heteroclinic and homoclinic orbits in singular perturbation problems
• Roughness of a discontinuous system
• Geometric singular perturbation theory for ordinary differential equations
• Structurally stable discontinuous vector fields in the plane.
• Canard cycles and center manifolds
• A method of desingularization for analytic two-dimensional vector field families
• Singular perturbation problems for time-reversible systems
• Relaxation oscillation and canard explosion

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