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Mathematics of Complexity and Dynamical Systems pp 1325–1336Cite as

Perturbation Theory for Non-smooth Systems

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Article Outline

Glossary

Definition of the Subject

Introduction

Preliminaries

Vector Fields near the Boundary

Generic Bifurcation

Singular Perturbation Problem in 2D

Future Directions

Bibliography

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Abbreviations

Non‐smooth dynamical system:

Systems derived from ordinary differential equations when the non‐uniqueness of solutions is allowed. In this article we deal with discontinuous vector fields in R n where the discontinuities are concentrated in a codimension‐one surface.

Bifurcation:

In a k‑parameter family of systems, a bifurcation is a parameter value at which the phase portrait is not structurally stable.

Typical singularity:

Are points on the discontinuity set where the orbits of the system through them must be distinguished.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Universidade Estadual de Campinas, Campinas, Brazil

    Marco Antônio Teixeira

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  1. Marco Antônio Teixeira
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Teixeira, M.A. (2012). Perturbation Theory for Non-smooth Systems. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_83

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