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Measuring the criticality of a Hopf bifurcation. / Uteshev, Alexei; Kalmár-Nagy, Tamás.

In: Nonlinear Dynamics, Vol. 101, No. 4, 09.2020, p. 2541-2549.

Research output: Contribution to journal › Article › peer-review

Harvard

Uteshev, A & Kalmár-Nagy, T 2020, 'Measuring the criticality of a Hopf bifurcation', Nonlinear Dynamics, vol. 101, no. 4, pp. 2541-2549. https://doi.org/10.1007/s11071-020-05914-x

APA

Uteshev, A., & Kalmár-Nagy, T. (2020). Measuring the criticality of a Hopf bifurcation. Nonlinear Dynamics, 101(4), 2541-2549. https://doi.org/10.1007/s11071-020-05914-x

Vancouver

Uteshev A, Kalmár-Nagy T. Measuring the criticality of a Hopf bifurcation. Nonlinear Dynamics. 2020 Sep;101(4):2541-2549. https://doi.org/10.1007/s11071-020-05914-x

Author

Uteshev, Alexei ; Kalmár-Nagy, Tamás. / Measuring the criticality of a Hopf bifurcation. In: Nonlinear Dynamics. 2020 ; Vol. 101, No. 4. pp. 2541-2549.

BibTeX

@article{e2075b653af54441998cf79d41a0b59d,
title = "Measuring the criticality of a Hopf bifurcation",
abstract = "This work is based on the observation that the first Poincar{\'e}–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.",
keywords = "Discriminant, Distance to bifurcation, Hopf bifurcation, MARGIN, DISTANCE, STABILITY, CLOSEST, ALGORITHMS, POINTS",
author = "Alexei Uteshev and Tam{\'a}s Kalm{\'a}r-Nagy",
note = "Uteshev, A., Kalm{\'a}r-Nagy, T. Measuring the criticality of a Hopf bifurcation. Nonlinear Dyn 101, 2541–2549 (2020). https://doi.org/10.1007/s11071-020-05914-x",
year = "2020",
month = sep,
doi = "10.1007/s11071-020-05914-x",
language = "English",
volume = "101",
pages = "2541--2549",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Measuring the criticality of a Hopf bifurcation

AU - Uteshev, Alexei

AU - Kalmár-Nagy, Tamás

N1 - Uteshev, A., Kalmár-Nagy, T. Measuring the criticality of a Hopf bifurcation. Nonlinear Dyn 101, 2541–2549 (2020). https://doi.org/10.1007/s11071-020-05914-x

PY - 2020/9

Y1 - 2020/9

N2 - 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.

AB - 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.

KW - Discriminant

KW - Distance to bifurcation

KW - Hopf bifurcation

KW - MARGIN

KW - DISTANCE

KW - STABILITY

KW - CLOSEST

KW - ALGORITHMS

KW - POINTS

UR - http://www.scopus.com/inward/record.url?scp=85090196520&partnerID=8YFLogxK

U2 - 10.1007/s11071-020-05914-x

DO - 10.1007/s11071-020-05914-x

M3 - Article

AN - SCOPUS:85090196520

VL - 101

SP - 2541

EP - 2549

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -

ID: 62122205