Phase Synchronization in the Globally Coupled Non linear chaotic Maps and the Scaling Theory
| Project/Area Number |
09640373
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
素粒子・核・宇宙線
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| Research Institution | Meiji University |
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Principal Investigator |
SHIMADA Tokuzo Meiji Univ. Physics Dept. Professor, 理工学部, 教授 (10162679)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | 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 中央極限値定理 / 周期 / 乱流 Turbulence / Cluster クラスタ / ポジネガスイッチ / 大域的写像素子結合模型 / 中型結合大域的結合模型 / 隠れた長時間相関 / 大数の法則の破れ |
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| Research Abstract |
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.
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Report
(4 results)
Research Products
(14 results)
