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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.

##### MSC:
 94C05 Analytic circuit theory
Full Text:
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