Robustness and stability of synchronized chaos: an illustrative model

Author

Sushchik, Mikhail M., Jr. ; Rulkov, Nikolai F. ; Abarbanel, Henry D I

Author_Institution

Inst. for Nonlinear Sci., California Univ., San Diego, La Jolla, CA, USA

Volume

44

Issue

10

fYear

1997

fDate

10/1/1997 12:00:00 AM

Firstpage

867

Lastpage

873

Abstract

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

Keywords

Lyapunov methods; chaos; nonlinear dynamical systems; parameter estimation; robust control; synchronisation; amplitude excursions; chaotic systems; coupled one dimensional chaotic maps; disturbances; fixed points; negative conditional Lyapunov exponents; parameter mismatch; robustness; stability; synchronized chaos; transversally unstable periodic orbits; transverse Lyapunov exponents; Chaos; Chaotic communication; Communication system control; Extraterrestrial measurements; Noise level; Noise robustness; Orbits; Robust stability; Sea measurements; Stability analysis;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.633875

Filename

633875