| Presentation | 2016-07-21 An evaluation of the shape of the Lorenz attractor embedded in the delay coordinate space with persistent homology Shotaro Tsuji, Kazuyuki Aihara, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | We conducted a numerical evaluation of the geometric shapes of the Lorenz attractor and the recon-structed Lorenz attractors in the delay-coordinate space with persistent homology. Takens' embedding theoremensures that the reconstructed attractor embeded in the delay-coordinate space with sufficiently high dimension isdiffeomorphic to the original attractor. However, under the condition of differmorphism, the shape of the attractormay deform greatly depending on the delay time. Then, we evaluated the relation between the shapes of the recon-structed attractors and the delay time with persistent homology. Moreover, we observed that there are a signi cantdifference between the optimal delay time calculated with persistent homology and that calculated from the mutualinformation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | delay-coordinate space / Takens' theorem / Persistent homology |
| Paper # | NLP2016-37 |
| Date of Issue | 2016-07-14 (NLP) |
| Conference Information | |
| Committee | NLP |
|---|---|
| Conference Date | 2016/7/21(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Hokkaido Univ. Centennial Hall |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Hisato Fujisaka(Hiroshima City Univ.) |
| Vice Chair | Masaharu Adachi(Tokyo Denki Univ.) |
| Secretary | Masaharu Adachi(Konan Univ.) |
| Assistant | Hiroyuki Asahara(Okayama Univ. of Science) / Toshihiro Tachibana(Shonan Inst. of Tech.) |
| Paper Information | |
| Registration To | Technical Committee on Nonlinear Problems |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | An evaluation of the shape of the Lorenz attractor embedded in the delay coordinate space with persistent homology |
| Sub Title (in English) | |
| Keyword(1) | delay-coordinate space |
| Keyword(2) | Takens' theorem |
| Keyword(3) | Persistent homology |
| 1st Author's Name | Shotaro Tsuji |
| 1st Author's Affiliation | The University of Tokyo(Univ. Tokyo) |
| 2nd Author's Name | Kazuyuki Aihara |
| 2nd Author's Affiliation | The University of Tokyo(Univ. Tokyo) |
| Date | 2016-07-21 |
| Paper # | NLP2016-37 |
| Volume (vol) | vol.116 |
| Number (no) | NLP-151 |
| Page | pp.pp.17-20(NLP), |
| #Pages | 4 |
| Date of Issue | 2016-07-14 (NLP) |