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Testing chaotic dynamics via Lyapunov exponents

✍ Scribed by Fernando Fernández-Rodríguez; Simón Sosvilla-Rivero; Julián Andrada-Félix

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
170 KB
Volume
20
Category
Article
ISSN
0883-7252

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✦ Synopsis

Abstract

We propose a new test to detect chaotic dynamics, based on the stability of the largest Lyapunov exponent from different sample sizes. This test is applied to the data used in the single‐blind controlled competition tests for non‐linearity and chaos that were generated by Barnett et al. (1997), as well as to several other chaotic series. The results suggest that the new test is particularly effective when compared to other stochastic alternatives (both linear and non‐linear). For large sample sizes the power of the test is one, although for small sample sizes it diminishes occasionally. Copyright © 2005 John Wiley & Sons, Ltd.

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The localization factor, which was first developed in solid state physics [1][2][3][4][5][6], has often been used to quantify vibration localization in mono-coupled nearly periodic structures [7][8][9][10][11][12]. The localization factor is the average exponential decay rate of the vibration amplit