The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Cet article propose une nouvelle méthode pour obtenir numériquement des multiplicateurs de Floquet qui caractérisent la stabilité des orbites périodiques des équations différentielles ordinaires. Pour des orbites périodiques suffisamment lisses, nous pouvons calculer les multiplicateurs de Floquet en utilisant certaines méthodes numériques standards avec suffisamment de précision. Cependant, il a été signalé que ces méthodes pouvaient produire des résultats incorrects dans certaines conditions. Dans ce travail, nous proposons une nouvelle méthode itérative pour calculer les multiplicateurs de Floquet en utilisant les vecteurs propres des solutions matricielles des équations variationnelles. Des exemples numériques montrent l'efficacité de la méthode proposée.
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Yu NUREKI, Sunao MURASHIGE, "Computation of Floquet Multipliers Using an Iterative Method for Variational Equations" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 5, pp. 1331-1338, May 2009, doi: 10.1587/transfun.E92.A.1331.
Abstract: This paper proposes a new method to numerically obtain Floquet multipliers which characterize stability of periodic orbits of ordinary differential equations. For sufficiently smooth periodic orbits, we can compute Floquet multipliers using some standard numerical methods with enough accuracy. However, it has been reported that these methods may produce incorrect results under some conditions. In this work, we propose a new iterative method to compute Floquet multipliers using eigenvectors of matrix solutions of the variational equations. Numerical examples show effectiveness of the proposed method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.1331/_p
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@ARTICLE{e92-a_5_1331,
author={Yu NUREKI, Sunao MURASHIGE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Computation of Floquet Multipliers Using an Iterative Method for Variational Equations},
year={2009},
volume={E92-A},
number={5},
pages={1331-1338},
abstract={This paper proposes a new method to numerically obtain Floquet multipliers which characterize stability of periodic orbits of ordinary differential equations. For sufficiently smooth periodic orbits, we can compute Floquet multipliers using some standard numerical methods with enough accuracy. However, it has been reported that these methods may produce incorrect results under some conditions. In this work, we propose a new iterative method to compute Floquet multipliers using eigenvectors of matrix solutions of the variational equations. Numerical examples show effectiveness of the proposed method.},
keywords={},
doi={10.1587/transfun.E92.A.1331},
ISSN={1745-1337},
month={May},}
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TY - JOUR
TI - Computation of Floquet Multipliers Using an Iterative Method for Variational Equations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1331
EP - 1338
AU - Yu NUREKI
AU - Sunao MURASHIGE
PY - 2009
DO - 10.1587/transfun.E92.A.1331
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2009
AB - This paper proposes a new method to numerically obtain Floquet multipliers which characterize stability of periodic orbits of ordinary differential equations. For sufficiently smooth periodic orbits, we can compute Floquet multipliers using some standard numerical methods with enough accuracy. However, it has been reported that these methods may produce incorrect results under some conditions. In this work, we propose a new iterative method to compute Floquet multipliers using eigenvectors of matrix solutions of the variational equations. Numerical examples show effectiveness of the proposed method.
ER -