Abstract
Some aspects of the bifurcations of a modified van der Pol oscillator are considered. We focus our attention on the bifurcations related to a double-zero degeneracy in the linear part of the equilibrium point in the origin. The analysis of the corresponding normal form shows the possibility of additional degeneracy in the nonlinear part, which leads us to study a 3-parameter family of planar vector fields whose bifurcation set is described.
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References
Carr, J. (1981) Applications of Centre Manifold Theory, Springer—Verlag, Heidelberg Berlin New—York.
Dumortier, F., Roussarie, R. and Sotomayor, J. (1987) `Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3’, Ergod. Th. Dynam. Sys., 7, 375–413.
Freire, E., G.Franquelo, L., Aracil, J. (1984) `Periodicity and Chaos in an Autonomous Electronic System’, IEEE Transactions on Circuits and Systems, Vol. CAS-31, No. 3, pp. 237–247.
Freire, E., Gamero, E., Ponce, E. (1989) `An Algorithm for Symbolic Computation of Hopf Bifurcation’, Computers and Mathematics, Eds. E. Kaltofen S.M. Watt, Springer—Verlag, pp. 109–118.
Gamero, E., Freire, E., Ponce, E. (1991) `On the Normal Forms for Planar Systems with Nilpotent Linear Part’ (see this volume).
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© 1991 Birkhäuser Verlag Basel
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Rodríguez-Luis, A.J., Freire, E., Ponce, E. (1991). On a Codimension 3 Bifurcation Arising in an Autonomous Electronic Circuit. In: Seydel, R., Schneider, F.W., Küpper, T., Troger, H. (eds) Bifurcation and Chaos: Analysis, Algorithms, Applications. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 97. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7004-7_39
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DOI: https://doi.org/10.1007/978-3-0348-7004-7_39
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7006-1
Online ISBN: 978-3-0348-7004-7
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