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

全局耦合非线性混沌映射中的相位同步和标度理论

基本信息

批准号：
09640373
负责人：
SHIMADA Tokuzo
金额：
$ 0.64万
依托单位：
Meiji University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640373/
关键词：
Glogally Coupled Maps turbulence intelligence complex system foliation windows cluster-attractor symmetry breaking Synchronization Globally Coupled Maphattice Linear stability(線形安定性)Low of Large numbers 大数の法則 Central Limit theorem

项目摘要

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.

我们对其湍流状态中的全球耦合地图晶格（GCML）进行了广泛的统计调查，该统计晶格被视为具有异常统计特性的系统；地图的平均场即使是在违反大量定律（隐藏连贯性）的热动力学极限的情况下也会波动。我们的发现可以汇总如下1。即使地图之间的耦合设置在湍流方案中极小，但我们发现那里出现了显着的集群吸引子，其中地图分为几个簇，并且在一定周期性中相互振荡的簇。最显着的周期性表现是在周期运动（P3C3 MSCA）中最大的对称三聚簇吸引子，由于种群对称性，平均场波动几乎可以忽略不计。2。如果将耦合设置为略高于MSCA的耦合，则出现相关的吸引态，其中簇的数量减少，但群集轨道大约相同。在这里，平均场波动异常增强3。我们可以成功得出调整条件，该调整条件确定了在给定的非线性地图上形成各种聚类状态的必要耦合。 GCML的湍流制度中的控制动力学是元素逻辑图的周期性窗口的叶面。隐藏的含量可能被认为是最适中的周期性表现。我们的调整条件预测了模型参数空间中的曲线，这些曲线将这些GCML与不同的非线性和耦合联系在一起，但表现出相同的周期性群集状态。 GCML是智能活动的基本模型。我们认为，如上所述的我们的发现对于该研究领域的未来进步至关重要，因为它们简洁地说，即使在非常弱的耦合下，大型复杂系统也可以形成同步状态。