| Presentation | 2005-01-24 Construction of Bifurcation Surface by Newton-Homotopy Method Hiroki YOSHII, Tetsushi UETA, Hiroshi KAWAKAMI, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This report investigates problems about construction of bifurcation surface in three dimensional parameter space. Conventionally solving the shooting algorithm in this space using Newton's method seems to be difficult since it is very sensitive for the initial values including parameter values and state variables. We have tried to collect many planar bifurcation diagrams to build a 3D surface, like the computer tomography, but it is a burden toil, besides, it consumes much time and efforts. In this paper, we propose an new and efficient method to obtain such surfaces. Firstly we provide a rectangle patch as an initial state by using conventional shooting method. Secondly we seek candidate patches around the inital patch. The seeking path forms a concentric circle. Vertices of a candidate patch are estimated by using normal vector. and locations of vertices of the reference patch and other estimated patches. Newton-homotopy method is used to correct the estimation error. As an illustrated example, we show a bifurcation surface of Duffing's equation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | bifurcation curve / Newton-Homotopy method / visualization |
| Paper # | NLP2004-91 |
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| Conference Information | |
| Committee | NLP |
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| Conference Date | 2005/1/17(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| 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) | Construction of Bifurcation Surface by Newton-Homotopy Method |
| Sub Title (in English) | |
| Keyword(1) | bifurcation curve |
| Keyword(2) | Newton-Homotopy method |
| Keyword(3) | visualization |
| 1st Author's Name | Hiroki YOSHII |
| 1st Author's Affiliation | Faculty of Engineering, Tokushima University() |
| 2nd Author's Name | Tetsushi UETA |
| 2nd Author's Affiliation | Center for Advanced Information Technology, Tokushima University |
| 3rd Author's Name | Hiroshi KAWAKAMI |
| 3rd Author's Affiliation | Faculty of Engineering, Tokushima University |
| Date | 2005-01-24 |
| Paper # | NLP2004-91 |
| Volume (vol) | vol.104 |
| Number (no) | 583 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |