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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Semi-algebraic Description of the Equilibria of Dynamical Systems
verfasst von : Changbo Chen, Marc Moreno Maza
Erschienen in: Computer Algebra in Scientific Computing
Verlag: Springer Berlin Heidelberg
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We study continuous dynamical systems defined by autonomous ordinary differential equations, themselves given by parametric rational functions. For such systems, we provide semi-algebraic descriptions of their hyperbolic and non-hyperbolic equilibria, their asymptotically stable hyperbolic equilibria, their Hopf bifurcations. To this end, we revisit various criteria on sign conditions for the roots of a real parametric univariate polynomial. In addition, we introduce the notion of
comprehensive triangular decomposition
of a semi-algebraic system and demonstrate that it is well adapted for our study.