| Presentation | 2013-05-28 Pattern Categorization of the Bifurcation of Quasi-Periodic Solutions by using Covariant Lyapunov Bundle Kyohei KAMIYAMA, Motomasa KOMURO, Tetsuro ENDO, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In continuous dynamical system, a periodic orbit becomes a fix point by taking a certain Poincare section. Therefore, by calculating the eigenvalues and eigenvectors of the fixed point, we can calculate local stability and progressing direction. In contrast, a quasi-periodic solution (two-torus) becomes an invariant closed curve (ICC) in Poincare section. For an ICC one can calculate Lyapunov exponents which are generalization of the eigenvalues of a fixed point. However, there is no defined value corresponding to the eigenvectors of a fixed point. In this paper, we define covariant Lyapunov vector (CLV) at each mapped point of ICC, and succeed to draw a bundle of CLV along the ICC. This is a part of tangent bundle formed by tangent space of ICC. Therefore, we call it "covariant Lyapunov bundle." In this research, we classify various local bifurcations of ICC by using covariant Lyapunov vectors and Lyapunov exponents. As examples, we introduce the behavior of CLB for saddle-node bifurcation, pitchfork bifurcation, period-doubling bifurcation of type 1 (increase of winding number), that of type 2 (collapse of stability), and Neimark-Sacker bifurcation by using continuous dynamical systems. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | covariant Lyapunov bundle / covariant Lyapunov vector / Lyapunov exponent / invariant closed curve / quasi-periodic solution / local bifurcation |
| Paper # | NLP2013-23 |
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| Committee | NLP |
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| Conference Date | 2013/5/20(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Nonlinear Problems (NLP) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Pattern Categorization of the Bifurcation of Quasi-Periodic Solutions by using Covariant Lyapunov Bundle |
| Sub Title (in English) | |
| Keyword(1) | covariant Lyapunov bundle |
| Keyword(2) | covariant Lyapunov vector |
| Keyword(3) | Lyapunov exponent |
| Keyword(4) | invariant closed curve |
| Keyword(5) | quasi-periodic solution |
| Keyword(6) | local bifurcation |
| 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 | 2013-05-28 |
| Paper # | NLP2013-23 |
| Volume (vol) | vol.113 |
| Number (no) | 69 |
| Page | pp.pp.- |
| #Pages | 4 |
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