NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2007, Vol.10, No.1, pp.79-85


Computational Algebra and Limit Cycles Bifurcations in Polynomial Systems.
Valery G. Romanovski

We give a simple proof of Bautin's theorem on the cyclicity of the quadratic system of differential equations [2]. The proof is based on elementary algorithms of computational algebra. Namely, we show that the variety of the Bautin ideal coincides with the variety of the ideal generated by the first three focus quantities and the ideal is a radical one. This yields a bound for the cyclicity obtained by Bautin.
Key words: limit cycles, cyclicity, center problem

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