Very long transients in globally coupled maps
Fritz-Haber-Institut der Max-Planck-Gesellschaft
Faradayweg 4-6, 14195 Berlin, Germany
Accepted: 6 April 2000
The general classification of the phase-space of globally coupled logistic maps, introduced by Kaneko (see Kaneko K. Phys. Rev. Lett. 63 (1989)219; Physica D 41 (1990) 137), is substantially modified. Our numerical investigations show that in the parameter region of the former “glassy" phase the asymptotic behaviour actually corresponds to single attractors or networks of several Milnor attractors described by partitions with only a few clusters. This asymptotic regime is found after very long transients and persists when weak noises are introduced. The prevalence of cluster partitions with a large number of clusters, proportional to the size of the system, was previously reported in this region (Kaneko K. Phys. Rev. Lett. 63 (1989)219; Physica D 41 (1990) 137) and considered as its defining property.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 05.45.Xt – Synchronization; coupled oscillators / 05.40.Ca – Noise
© EDP Sciences, 2000