Abstract
Computing certain relevant coefficients for Hopf bifurcations is of interest to characterize the bifurcation (ie, to determine direction, kind, stability and number of eventual emanating branches). The calculations involved are tedious and very prone to error, thereby being nearly impossible to do them by hand.
Using an algorithm previously developed by Freire et al, which is well suited for symbolic computation, a MAPLE procedure has been developed and tested.
In particular, the explicit general expressions of the coefficients of Hopf bifurcation up to fifth degree have been obtained. For specific cases, higher degree results are also reachable.
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© 1991 Birkhäuser Verlag Basel
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Ponce-Núñez, E.J., Gamero, E. (1991). Generating Hopf Bifurcation Formulae with MAPLE. 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_38
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DOI: https://doi.org/10.1007/978-3-0348-7004-7_38
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7006-1
Online ISBN: 978-3-0348-7004-7
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