On Coupling Strength of Coupled Map Lattices

藕合網格上的藕合強度

黃俊銘(Jing-Ming Huang)

指導教授 ： 林文偉 ； 莊重

國立清華大學/理學院/數學系/碩士(2008年)

https://doi.org/10.6843/NTHU.2008.00447

摘要

這篇論文主要研究當藕合強度ｃ變化時藕合網格的動態行為。主要結果如下
１. 當ｃ很小的時候，我們可以儘可能的找到snap-back repellers。
２. 我們可以刻劃出當藕合網格有局部同步現象時ｃ的範圍，而此範圍可以用中心點、左半徑以及右半徑描述出來，而當ｃ等於此中心點的值時，收斂到同步區域的速度將會最快。除此之外，我們也可驗證，此中心點只跟藕合網格上質點的個數，以及藕合矩陣Ｇ有關，而跟未藕合前的動態行為ｆ無關。

關鍵字

藕合強度 ； 藕合網格 ； 同步

並列摘要

We study the dynamics of coupled map lattices (CMLs) as the coupling strength c varies. Our main results are as follows. First, we show that for small c, as many snap-back repellers as possible can be obtained. Second, we study the “intermediate” range of c. In particular, the optimal range of c for getting local synchronization of CMLs can be explicitly constructed by indentifying its center, left and right radii. The center of coupling strength for local synchronization gives the fastest convergence rate of the initial values toward synchronous manifold. Moreover, we prove that the center depends on the number of nodes and the connectivity topology G, and is independent of the choice of uncoupled dynamics f

並列關鍵字

coupling strength ； coupled map lattices ； synchronization

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