Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 239-255

Synchronization in ensembles of coupled maps with a major element

Iryna Omelchenko,1 Yuri Maistrenko,1 and Erik Mosekilde2

1Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, Kyiv–4 01601, Ukraine
2Department of Physics, Technical University of Denmark, Lyngby 2800 Kgs., Denmark

Received 16 March 2005

Copyright © 2005 Iryna Omelchenko et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper investigates the conditions for full and partial synchronization in systems of coupled chaotic maps that include the presence of a major element, that is, an element that interacts with all the other elements of the system. We consider a system which consists of two globally coupled populations of one-dimensional maps that interact via a major element. The presence of this element can induce synchronization in both of the globally coupled populations even though they operate in different states. If a parameter mismatch is introduced between two populations of uncoupled maps, the presence of a major element is found to provide for the existence of states in which peripheral elements with different parameter values display similar dynamics.