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Cimatti, Giovanni ; Feireisl, Eduard
A simple model of thermoelectric oscillations. (English). Applications of Mathematics, vol. 40 (1995), issue 2, pp. 147-158
MSC: 34C15, 34C25, 78A97 | MR 1314484 | Zbl 0833.34033 | DOI: 10.21136/AM.1995.134285
Keywords:
thermistor; time-periodic solution; Hopf bifurcation
Summary:
A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
References:
[1] J. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. Springer-Verlag, New York Inc., 1983. MR 0709768
[2] F.J. Hyde: Thermistors. Iliffe Book, London, 1971.
[3] J.J. Marsden, M. McCracken: The Hopf Bifurcation and its Application. Springer-Verlag, New York Inc., 1976. MR 0494309
[4] Ambrosetti, G. Prodi: A Primer in Nonlinear Analysis. Academic Press.
[5] R.W.A. Scarr, R.A. Setterington: Thermistors, their theory, manufacture and application. The Institution of Electrical Engineers 3176 M, Jan., 1960.
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