This work is based on the observation that the first Poincaré–Lyapunov constant is a quadratic function of the coefficients of the two-dimensional vector field at a Hopf bifurcation. From a given parameter point, we find the distance to the “Hopf quadric.” This distance provides a measure of the criticality of the Hopf bifurcation. The viability of the approach is demonstrated through numerical examples.

Original languageEnglish
Pages (from-to)2541-2549
Number of pages9
JournalNonlinear Dynamics
Volume101
Issue number4
Early online date3 Sep 2020
DOIs
StatePublished - Sep 2020

    Scopus subject areas

  • Applied Mathematics

    Research areas

  • Discriminant, Distance to bifurcation, Hopf bifurcation, MARGIN, DISTANCE, STABILITY, CLOSEST, ALGORITHMS, POINTS

ID: 62122205