The invariant tori for the 2-mode damped, driven sine-Gordon ODE

Chi-Jer Yu; Jong Eao Lee

doi:10.1142/S0218127403006662

The invariant tori for the 2-mode damped, driven sine-Gordon ODE

Chi-Jer Yu^*
, Jong Eao Lee

^*此作品的通信作者

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研究成果: Article › 同行評審

摘要

An algorithm for presenting the entire branches of quasiperiodic solutions starting from the bifurcation points in the branches of periodic solutions in an interval of parameters for the 2-mode damped, driven sine-Gordon ODE is discussed. The algorithm is applied to the other Hopf bifurcation point on the same branch. It is observed that the invariant curves in the new branch behave in opposite ways, i.e. they are relatively much more stable in dynamics yet their geometry is unstable.

原文	English
頁（從 - 到）	505-509
頁數	5
期刊	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
卷	13
發行號	2
DOIs	https://doi.org/10.1142/S0218127403006662
出版狀態	Published - 2月 2003

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abstract = "An algorithm for presenting the entire branches of quasiperiodic solutions starting from the bifurcation points in the branches of periodic solutions in an interval of parameters for the 2-mode damped, driven sine-Gordon ODE is discussed. The algorithm is applied to the other Hopf bifurcation point on the same branch. It is observed that the invariant curves in the new branch behave in opposite ways, i.e. they are relatively much more stable in dynamics yet their geometry is unstable.",

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N2 - An algorithm for presenting the entire branches of quasiperiodic solutions starting from the bifurcation points in the branches of periodic solutions in an interval of parameters for the 2-mode damped, driven sine-Gordon ODE is discussed. The algorithm is applied to the other Hopf bifurcation point on the same branch. It is observed that the invariant curves in the new branch behave in opposite ways, i.e. they are relatively much more stable in dynamics yet their geometry is unstable.

AB - An algorithm for presenting the entire branches of quasiperiodic solutions starting from the bifurcation points in the branches of periodic solutions in an interval of parameters for the 2-mode damped, driven sine-Gordon ODE is discussed. The algorithm is applied to the other Hopf bifurcation point on the same branch. It is observed that the invariant curves in the new branch behave in opposite ways, i.e. they are relatively much more stable in dynamics yet their geometry is unstable.

KW - Bifurcation

KW - Invariant

KW - Numerical

KW - Quasiperiodic

KW - Tori

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JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 2

ER -

The invariant tori for the 2-mode damped, driven sine-Gordon ODE

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