Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 239-255
doi:10.1155/DDNS.2005.239
Synchronization in ensembles of coupled maps
with a major element
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.
Abstract
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.