Synchronization of globally coupled non - identical maps with inhomogeneous delayed interactions

We study the synchronization of a coupled map lattice consisting of a one-dimensional chain 9 of logistic maps. We consider global coupling with a time-delay that takes into account the nite velocity of propagation of interactions. We recently showed that clustering occurs for 11 weak coupling, while for strong coupling the array synchronizes into a global state where each element sees all other elements in its current, present state (Physica A 325 (2003) 186; Phys. 13 Rev. E 67 (2003) 056219). In this paper, we study the e ects of in-homogeneities, both in the individual maps, which are non-identical maps evolving in period-2 orbits, and in the connec15 tion links, which have non-uniform strengths. We nd that the global synchronization regime occurring for strong coupling is robust to heterogeneities: for strong enough average coupling 17 the inhomogeneous array still synchronizes in a global state in which each element sees the other elements in positions close to its current state. However, the clustering behaviour occur19 ring for small coupling is sensitive to inhomogeneities and di ers from that occurring in the homogeneous array. 21 c © 2004 Elsevier B.V. All rights reserved.