Normal forms for constrained nonlinear differential equations. I. Theory

Author

Chua, Leon O. ; Oka, Hiroe

Author_Institution

Dept. of Electr. Eng & Comput. Sci., California Univ., Berkeley, CA, USA

Volume

35

Issue

7

fYear

1988

fDate

7/1/1988 12:00:00 AM

Firstpage

881

Lastpage

901

Abstract

The theory of normal forms for smooth vector fields is system nonlinear differential-algebraic equations. Such equations are widely encountered in practical circuits and systems when parasitics play an important role in the system´s qualitative behavior. Such parasitics are a called small parameters in the associated singular perturbation problem. The approach taken from here is completely different form the literature on singular perturbation and is based on the general framework described by L.D. Chua and H. Kokuba (see ibid., vol. 35, no. 7, p. 863-880. 1988), namely, the calculation of infinitesimal deformations. A coordinate-free formulation for constrained equations give a local classification according to the extent of the degeneracy of the original constrained equation

Keywords

nonlinear differential equations; vectors; constrained nonlinear differential equations; coordinate-free formulation; degeneracy; general framework; infinitesimal deformations; local classification; normal forms; parasitics; qualitative behavior; singular perturbation problem; smooth vector fields; theory; Circuits and systems; Constraint theory; Differential equations; Ear; Mathematics; Nonlinear circuits; Nonlinear equations; Orbits;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.1834

Filename

1834