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Impasse points. Part II: Analytical aspects
Author(s) -
Chua Leon O.,
Deng AnChang
Publication year - 1989
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490170303
Subject(s) - jacobian matrix and determinant , transversality , mathematics , limit (mathematics) , singular point of a curve , image (mathematics) , point (geometry) , differential equation , differential (mechanical device) , matrix (chemical analysis) , algebraic number , mathematical analysis , pure mathematics , topology (electrical circuits) , computer science , combinatorics , geometry , physics , materials science , artificial intelligence , composite material , thermodynamics
An impasse point of the implicit differential‐algebraic system. Has been characterized in Part I of this paper as a limit point of an induced solution curveIn this paper we use the Liapunov‐Schmidt procedure to derive an analytical test for identifying impasse points. We also invoke the transversality theory from differential topology to show that almost all singular points (X o , y o ) of S, which occur when the Jacobian matrixis singular, are in fact impasse points.