Measuring the criticality of a Hopf bifurcation

Measuring the criticality of a Hopf bifurcation

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 cri...

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Veröffentlicht in:Nonlinear dynamics 2020-09, Vol.101 (4), p.2541-2549
Hauptverfasser: Uteshev, Alexei, Kalmár-Nagy, Tamás
Format: Artikel
Sprache:eng
Schlagworte:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Engineering, Mechanical
Mechanical Engineering
Mechanics
Original Paper
Science & Technology
Technology
Vibration
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Zusammenfassung: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05914-x