| Presentation | 2014-12-04 Bifurcation Avoidance of Stable Periodic Oscillations in Continuous-Time Duffing Equation Tomohiro OTSU, Ken'ichi FUJIMOTO, Tetsushi UETA, Kazuyuki AIHARA, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | We previously proposed a parametric control method to avoid bifurcations of stable fixed and periodic points in discrete-time dynamical systems. The parameter regulation to avoid bifurcations is derived from an optimization problem on the maximum local Lyapunov exponent and the method of steepest descent. This method allows us to predict occurrence of bifurcations caused by unexpected parameter change and to avoid it without directly analyzing bifurcations in advance. In this report, on the basis of the ideas and a stroboscopic mapping that discretizes the trajectory of a continuous-time solution, we propose a methodology to avoid bifurcations of stable periodic oscillations in continuous-time non-autonomous dynamical systems. We also demonstrate that the proposed method can avoid bifurcations of stable periodic solutions in Duffing equation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Maximum local Lyapunov exponent / stable periodic oscillation / avoidance of bifurcation / continuous-time non-autonomous dynamical system / stroboscopic mapping |
| Paper # | NLP2014-111 |
| Date of Issue |
| Conference Information | |
| Committee | NLP |
|---|---|
| Conference Date | 2014/11/26(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | |
| Vice Chair | |
| Secretary | |
| Assistant | |
| Paper Information | |
| Registration To | Nonlinear Problems (NLP) |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Bifurcation Avoidance of Stable Periodic Oscillations in Continuous-Time Duffing Equation |
| Sub Title (in English) | |
| Keyword(1) | Maximum local Lyapunov exponent |
| Keyword(2) | stable periodic oscillation |
| Keyword(3) | avoidance of bifurcation |
| Keyword(4) | continuous-time non-autonomous dynamical system |
| Keyword(5) | stroboscopic mapping |
| 1st Author's Name | Tomohiro OTSU |
| 1st Author's Affiliation | Graduate School of Advanced Technology and Science, the University of Tokushima() |
| 2nd Author's Name | Ken'ichi FUJIMOTO |
| 2nd Author's Affiliation | Institute of Health Biosciences, the University of Tokushima |
| 3rd Author's Name | Tetsushi UETA |
| 3rd Author's Affiliation | Center for Administration of Information Technology, the University of Tokushima |
| 4th Author's Name | Kazuyuki AIHARA |
| 4th Author's Affiliation | Institute of Industrial Science, the University of Tokyo |
| Date | 2014-12-04 |
| Paper # | NLP2014-111 |
| Volume (vol) | vol.114 |
| Number (no) | 348 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |