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CASC
2011
Springer

Semi-algebraic Description of the Equilibria of Dynamical Systems

7 years 6 months ago
Semi-algebraic Description of the Equilibria of Dynamical Systems
Abstract. 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.
Changbo Chen, Marc Moreno Maza
Added 13 Dec 2011
Updated 13 Dec 2011
Type Journal
Year 2011
Where CASC
Authors Changbo Chen, Marc Moreno Maza
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