| Presentation | 2013-01-24 Calculating finite-time Lyapunov exponents in time delayed dynamical systems Kazutaka KANNO, Atsushi UCHIDA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Lyapunov exponents represents a exponential expansion (construction) rate of a infinitesimal perturba-tion to an orbit of a dynamical system, which are asymptotic values over an attractor of the system. Finite-time Lyapunov exponents have been proposed to quantify the exponential expansion (construction) rate for finite orbits. We can obtain some information which is useful for classification of chaos dynamics, chaos control, and prediction. However, a method for calculation of the finite-time Lyapunov exponents in time-delayed dynamical systems have not been well established yet because of the difficulty of calculating Lyapunov exponents in time-delayed high-dimen-sional systems. We present a method for calculating the finite-time Lyapunov exponents in time-delayed dynamical systems, and apply it to a Mackey-Glass model, an optpelectromc feedback laser system and a Lang-Kobayashi equation for a semiconductor laser with optical feedback. We investigate standard deviation of the finite-time Lya-punov exponents for the variation of a delay time and a length of a orbit. It is found that the standard deviation approaches to zero as finite time L, and this approach is as L-v. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | time delayed dynamical systems / finite-time Lyapunov exponents / chaos |
| Paper # | NLP2012-116,NC2012-106 |
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| Committee | NLP |
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| Conference Date | 2013/1/17(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) | Calculating finite-time Lyapunov exponents in time delayed dynamical systems |
| Sub Title (in English) | |
| Keyword(1) | time delayed dynamical systems |
| Keyword(2) | finite-time Lyapunov exponents |
| Keyword(3) | chaos |
| 1st Author's Name | Kazutaka KANNO |
| 1st Author's Affiliation | Department of Information and Computer Sciences, Saitama University() |
| 2nd Author's Name | Atsushi UCHIDA |
| 2nd Author's Affiliation | Department of Information and Computer Sciences, Saitama University |
| Date | 2013-01-24 |
| Paper # | NLP2012-116,NC2012-106 |
| Volume (vol) | vol.112 |
| Number (no) | 389 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |