Semi-algebraic Description of the Equilibria of Dynamical Systems

  • Changbo Chen
  • Marc Moreno Maza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)


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.


Hopf Bifurcation Prion Disease Centre Manifold Theory Hyperbolic Equilibrium Pure Imaginary Eigenvalue 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Changbo Chen
    • 1
  • Marc Moreno Maza
    • 1
  1. 1.The University of Western OntarioLondonCanada

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