×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Introduction to Nonlinear Networks, McGraw-Hill, New York, 1969.
[2] and , Linear and Nonlinear Circuits, McGraw-Hill, New York, 1987. · Zbl 0631.94017
[3] Chua, Int. j. cir. theor. appl. 11 pp 161– (1983)
[4] Chua, Int. j. cir. theor. appl. 12 pp 337– (1984)
[5] Chua, IEEE Trans. Circuits and Systems CAS-32 pp 46– (1985)
[6] Chua, Int. j. cir. theor. appl. 13 pp 235– (1985)
[7] Chua, IEEE Trans. Circuit Theory CT-18 pp 520– (1971)
[8] Chua, Int. j. cir. theor. appl. 6 pp 211– (1978)
[9] Sastry, IEEE Trans. Circuits and Systems CAS-28 pp 1109– (1981)
[10] Haggman, IEEE Trans. Circuits and Systems CAS-31 pp 1015– (1984)
[11] ’On network perturbation of electrical circuits and singular perturbation of dynamical systems’, in Chaos, Fructals and Dynamics, and (eds), Dekker, New York, 1987, pp. 197–212.
[12] ’Constrained equations: a study of implicit differential equations and their discontinuous solutions’, in Lecture Notes in Mathematics, Vol. 525, Springer-Verlag, 1976, pp. 143–234.
[13] Chua, IEEE Trans. on Circuits and Systems CAS-35 pp 881– (1988)
[14] Brayton, Proc. IEEE 60 pp 98– (1972)
[15] Gear, Comm. ACM 14 pp 176– (1971)
[16] and , Computer-Aided Analysis of Electronic Circuits, Prentice-Hall, Englewood Cliff, NJ, 1975. · Zbl 0358.94002
[17] Differential Geometry, Harper and Row, New York, 1987.
[18] and , Nonlinear Differential Equations of Higher Order, Noordhoff, the Netherlands, 1974.
[19] Singular Points of Smooth Mappings, Pitman, London, 1979. · Zbl 0426.58001
[20] Ushida, Int. j. cir. theor. appl. 12 pp 1– (1984)
[21] Instabilities and Catastrophes in Science and Engineering, Wiley, 1982.
[22] Chua, IEEE Trans. Circuits and Systems CAS-27 pp 1014– (1980)
[23] and , Nonlinear Circuits, Artech House, Boston, MA, 1986.
[24] ’SPICE2: a computer program to simulate semiconductor circuits’, ERL Memo M520, University of California, Berkeley, CA, 1975.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.