Clustering zones in the turbulent phase of a system of globally coupled chaotic maps.
The paper develops an approach to investigate the clustering phenomenon in the system of globally coupled chaotic maps first introduced by Kaneko in 1989. We obtain a relation between the transverse and longitudinal multipliers of the periodic clusters and prove the stability of these clusters for the case of symmetric, equally populated distributions between subclusters. Stable clusters emanate from the periodic windows of the logistic map and extend far into the turbulent phase. By numerical simulations we estimate a total basin volume of low-periodic clusters issued from the period-3 window and analyze the basin structure. The complement to the basin volume is ascribed to chaotic, very asymmetric high-dimensional clusters that are characterized by the presence of one or more leading clusters, accumulating about half of the oscillators while all the remaining oscillators do not cluster at all.
Maistrenko
Yu
Y
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska st., 3, 01601 Kyiv, Ukraine. maistrenko@imath.kiev.ua
Panchuk
A
A