Volume 52, Number 6, December II 2000
|Page(s)||615 - 619|
|Published online||01 September 2002|
Long transients and cluster size in globally coupled maps
Consejo Nacional de
Investigaciones Científicas y Técnicas, Centro Atómico Bariloche
8400 S.C. de Bariloche, Argentina
Corresponding author: firstname.lastname@example.org
Accepted: 18 October 2000
We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the ordered phase of these systems. The transient times necessary to reach the asymptotic states can be very long, especially very near the transition line separating the ordered and the coherent phases. We find that, where two clusters form, the distribution of their sizes corresponds to windows of regular or narrow-band chaotic behavior in the bifurcation diagram of a system of two degrees of freedom that describes the motion of two clusters, where the size of one cluster acts as a bifurcation parameter.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 05.45.Xt – Synchronization; coupled oscillators
© EDP Sciences, 2000
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