Presentation 2014-01-21
Bifurcation of 2-Torus and its Covariant Lyapunov Bundle Observed in Coupled Oscillator System
Kyohei KAMIYAMA, Motomasa KOMURO, Tetsuro ENDO,
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Abstract(in English) In this paper, we'd like to explain covariant Lyapunov bundle (CLB) which is generalization of eigen vector for high dimensional torus (2-torus and more). A coupled oscillator system is given as an example of CLB. In continuous dynamical system, the CLB is obtained in both flow and Poincare section. We mainly take up the CLB in Poincare section because of the interpretative simplicity for the qualitative change of characteristic of phase space. Furthermore, in this paper, the computation target of CLB is 2-torus in flow. 2-torus in flow represents 1-torus in Poincare section, this 1-torus is called invariant closed curve (ICC). A CLB is a set of the covariant Lyapunov vectors (CLV) which come out from each points of ICC, and generally, since a set of CLV shapes bundle, we call this CLB. We demonstrate the 2-torus Neimark-Sacker (2-Torus Neimark-Sacker, T^2NS) bifurcation in a coupled oscillator system, and clarify the relationship with asynchronous degeneration.
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Keyword(in English) covariant Lyapunov bundle / Lyapunov exponent / coupled oscillator system / quasi-periodic solution / Neimark-Sacker bifurcation / asynchronous degeneration
Paper # NLP2013-145
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Committee NLP
Conference Date 2014/1/14(1days)
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Registration To Nonlinear Problems (NLP)
Language JPN
Title (in Japanese) (See Japanese page)
Sub Title (in Japanese) (See Japanese page)
Title (in English) Bifurcation of 2-Torus and its Covariant Lyapunov Bundle Observed in Coupled Oscillator System
Sub Title (in English)
Keyword(1) covariant Lyapunov bundle
Keyword(2) Lyapunov exponent
Keyword(3) coupled oscillator system
Keyword(4) quasi-periodic solution
Keyword(5) Neimark-Sacker bifurcation
Keyword(6) asynchronous degeneration
1st Author's Name Kyohei KAMIYAMA
1st Author's Affiliation Electronics and Bioinfomatics, Meiji University()
2nd Author's Name Motomasa KOMURO
2nd Author's Affiliation Center for Fundamental Education, Teikyo University of Science
3rd Author's Name Tetsuro ENDO
3rd Author's Affiliation Electronics and Bioinfomatics, Meiji University
Date 2014-01-21
Paper # NLP2013-145
Volume (vol) vol.113
Number (no) 383
Page pp.pp.-
#Pages 3
Date of Issue