Title :
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
fDate :
10/1/1997 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
