Robustness and stability of synchronized chaos: an illustrative model

Synchronization of two chaotic systems is not guaranteed by having only negative conditional or transverse Lyapunov exponents. If there are transversally unstable periodic orbits or fixed points embedded in the chaotic set of synchronized motions, the presence of even very small disturbances from no...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 1997-10, Vol.44 (10), p.867-873
Main Authors: Sushchik, M.M., Rulkov, N.F., Abarbanel, H.D.I.
Format: Article
Language:English
Subjects:
Chaos
Chaotic communication
Communication system control
Extraterrestrial measurements
Noise level
Noise robustness
Orbits
Robust stability
Sea measurements
Stability analysis
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Summary:Synchronization of two chaotic systems is not guaranteed by having only negative conditional or transverse Lyapunov exponents. If there are transversally unstable periodic orbits or fixed points embedded in the chaotic set of synchronized motions, the presence of even very small disturbances from noise or inaccuracies from parameter mismatch can cause synchronization to break down and lead to substantial amplitude excursions from the synchronized state. Using an example of coupled one dimensional chaotic maps we discuss the conditions required for robust synchronization and study a mechanism that is responsible for the failure of negative conditional Lyapunov exponents to determine the conditions for robust synchronization.
ISSN:1057-7122
1558-1268
DOI:10.1109/81.633875