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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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

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

First available in Project Euclid: 5 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Regularization vector fields singular perturbation discontinuous vector fields sliding vector fields


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. https://projecteuclid.org/euclid.bbms/1228486412.

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