Local Lyapunov exponents for spatiotemporal chaos

1993 ◽  
Vol 3 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Arkady S. Pikovsky
Keyword(s):  
Lyapunov Exponents ◽  
Spatiotemporal Chaos

Synchronization of spatiotemporal chaos with positive conditional Lyapunov exponents

1997 ◽  
Vol 56 (2) ◽  
pp. 2272-2275 ◽  
Author(s):  
J. W. Shuai ◽  
K. W. Wong ◽  
L. M. Cheng
Keyword(s):  
Lyapunov Exponents ◽  
Spatiotemporal Chaos

Lyapunov Exponents

2016 ◽  
Author(s):  
Arkady Pikovsky ◽  
Antonio Politi
Keyword(s):  
Lyapunov Exponents

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

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