Phase Synchronization in the Globally Coupled Non linear chaotic Maps and the Scaling Theory

点击翻译按钮获取中文摘要

We performed an extensive statistical survey of Globally Coupled Map Lattice (GCML) in its turbulent regime, which had been regarded as a system with an anomalous statistical property; the mean field of the map fluctuates even at the thermo dynamical limit violating the law of large numbers (a hidden coherence) .Our findings may be summarized as follows.1. Even though the coupling between the maps is set extremely small in the turbulent regime, we found that there emerge remarkable cluster attractors, in which the maps split into a few clusters and the clusters mutually oscillate in a certain periodicity. The most remarkable periodicity manifestation is the maximally symmetric three-clustered attractor in period-three motion (p3c3 MSCA), where the mean field fluctuation is almost negligible due to the population symmetry.2. If the coupling is set slightly higher than that for the MSCA, there emerge associated attractor-states, where the number of the clusters has decreased but the cluster orbits are approximately the same. Here the mean field fluctuation is anomalously enhanced.3. We could successfully derive the tuning condition, which determines the necessary coupling at a given non-linearity of maps for the formation of various cluster states. The controlling dynamics in the turbulent regime of GCML is the foliation of the periodic windows of the element logistic map. The hidden-coherence may be regarded most modest periodicity manifestation. Our tuning condition predicts curves in the model parameter space, which link together those GCML with distinct non-linearity and coupling but exhibiting the same periodic cluster state. The GCML is a basic model for the intelligence activity. We consider that our findings as listed above are crucial for the future progress in this research field because they succinctly tell that a large complex system can form synchronized states even at the very weak coupling.