An introduction to the synchronization of chaotic systems: coupled skew tent maps

Author

Hasler, Martin ; Maistrenko, Yuri L.

Author_Institution

Dept. of Electr. Eng., Swiss Fed. Inst. of Technol., Lausanne, Switzerland

Volume

44

Issue

10

fYear

1997

fDate

10/1/1997 12:00:00 AM

Firstpage

856

Lastpage

866

Abstract

In this tutorial paper, various phenomena linked to the synchronization of chaotic systems are discussed using the simple example of two coupled skew tent maps. The phenomenon of locally riddled basins of attraction is explained using the Lyapunov exponents transversal to the synchronization manifold. The skew tent maps are coupled in two different ways, leading to quite different global dynamic behavior especially when the ideal system is perturbed by parameter mismatch or noise. The linear coupling leads to intermittent desynchronization bursts of large amplitude, whereas for the nonlinear coupling the synchronization error is asymptotically uniformly bounded

Keywords

Lyapunov methods; chaos; nonlinear dynamical systems; synchronisation; Lyapunov exponents; asymptotically uniformly bounded; chaotic system synchronization; coupled skew tent maps; global dynamic behavior; intermittent desynchronization bursts; linear coupling; locally riddled basins of attraction; nonlinear coupling; parameter mismatch; synchronization error; Chaos; Couplings; Helium; Mathematics; Nonlinear dynamical systems; Nonlinear systems; Physics; Signal processing; Testing; Transmitters;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.633874

Filename

633874