Synchronization of Discrete Time Dynamical Systems

• Published in: Journal of difference equations and applications Vol. 10; no. 13-15; pp. 1133 - 1138
• Main Author: Kloeden, P.E.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis GroupAbingdon, UK 01-11-2004
• Subjects: Discrete time dynamical system; Global attractor; Linear implicit Euler scheme; Primary 37B25; Secondary 39411; Synchronization
• ISSN: 1023-6198; 1563-5120
• DOI: 10.1080/10236190410001652775

The synchronization of two discrete time dynamical systems is considered, where the systems are described in terms of first order difference equations, each of which satisfies a global dissipativity condition and hence has a global attractor. It is shown that the coupled trajectories converge to each other as time increases for sufficiently large coupling coefficient and that the global attractor of the coupled system converges upper semi continuously as the coupling parameter increases to the diagonal of the product of the global attractor of a discrete time dynamical system for which the defining function is the average of those of the original uncoupled systems.