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Impasse points. I: Numerical aspects. (English) Zbl 0676.94022
Summary: Impasse point is an important phenomenon found in many nonlinear circuits and systems. Among other things, the presence of an impasse point \(Q\) implies that the circuit model is defective and must be remodelled by augmenting it with parasitic inductances and/or capacitances at appropriate locations in order to predict the bifurcation from slow to rapid motions (jump phenomenon) widely observed in practice. The presence of an impasse point \(Q\) also implies that a numerical simulation of the associated system of implicit differential-algebraic equations would give rise to an extraneous and random small-amplitude oscillation in the vicinity of \(Q\). The wave-form associated with this ‘fake’ oscillatory phenomenon depends on the error-controlled mechanism of the integration routine and can be detected using the results from this paper.
For Part II see the following review Zbl 0676.94023.

94C05 Analytic circuit theory
Full Text: DOI
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