Bulletin of the Belgian Mathematical Society - Simon Stevin

Sliding Vector Fields via Slow--Fast Systems

Jaume Llibre, Marco A. Teixeira, and Paulo R. da Silva

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Abstract

This paper concerns differential equation systems on $\mathbb R^n$ with discontinuous right--hand sides. We deal with non-smooth vector fields in $\mathbb R^n$ having a codimension-one submanifold $M$ as its discontinuity set. After a regularization of a such system and a global blow-up we are able to bring out some results that bridge the space between discontinuous systems and singularly perturbed smooth systems.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 15, Number 5 (2008), 851-869.

Dates
First available in Project Euclid: 5 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.bbms/1228486412

Mathematical Reviews number (MathSciNet)
MR2484137

Zentralblatt MATH identifier
05496980

Subjects
Primary: 34C20: Transformation and reduction of equations and systems, normal forms 34C26: Relaxation oscillations 34D15: Singular perturbations 34H05: Control problems [See also 49J15, 49K15, 93C15]

Keywords
Regularization vector fields singular perturbation discontinuous vector fields sliding vector fields

Citation

Llibre, Jaume; da Silva, Paulo R.; Teixeira, Marco A. Sliding Vector Fields via Slow--Fast Systems. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 5, 851--869. http://projecteuclid.org/euclid.bbms/1228486412.


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