Abstract
The Hopf bifurcation has become a widely used method in the study of periodic oscillations of nonlinear dynamical systems. The purpose of this paper is not to carry out a direct symbolic algebraic manipulation of formulae characterizing this bifurcation (direction, stability and amplitudes of bifurcating periodic orbits, ...). It is planned to develop a recursive algorithm well suited to symbolic computation implementation, which is based upon the normal form approach and supplies the necessary information to characterize generalized Hopf bifurcations.
An efficient procedure to obtain the normal form corresponding to a Hopf bifurcation is presented; it is based upon the use of Lie transforms. The calculations are arranged in a recursive scheme using complex variables and so the computational effort is optimized. The devised algorithm is implemented on REDUCE 3.2 and applied to several examples.
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Freire, E., Gamero, E., Ponce, E. (1989). An Algorithm for Symbolic Computation of Hopf Bifurcation. In: Kaltofen, E., Watt, S.M. (eds) Computers and Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9647-5_14
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DOI: https://doi.org/10.1007/978-1-4613-9647-5_14
Publisher Name: Springer, New York, NY
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