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

^*Corresponding author for this work

Department of Applied Mathematics

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

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.

Original language	English
Pages (from-to)	505-509
Number of pages	5
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	13
Issue number	2
DOIs	https://doi.org/10.1142/S0218127403006662
State	Published - Feb 2003

Keywords

Bifurcation
Invariant
Numerical
Quasiperiodic
Tori

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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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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.

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KW - Numerical

KW - Quasiperiodic

KW - Tori

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

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Keywords

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