臺灣國際科展

同步現象的研究

科展類別
臺灣國際科展
屆次
2006年
科別
物理科
學校名稱
國立臺灣師範大學附屬高級中學
指導老師
王存雄
作者
章學元、劉傑瑋
關鍵字
同步現象,解析能力

摘要或動機

In our daily life, objects and the contacts between objects they will have mutually affect each other, some initially chaotic systems after a sufficient amount of time will mutually correct each other, and finally achieve synchronization (example: the speed of bird and fish migration, market prices, infantry…), although some are unable to achieve this. We will illustrate and explain the synchronization system, its process and discover the conditions for synchronization. Using linking concepts, we will integrate the coupled map lattices with global coupling and coupled map lattices with intermediate-range models into a synchronization mode in order to simulate a synchronization system. We first used a small system of n≦50 to obtain results that will demonstrate the linking concepts: 1. The more chaotic a system, a longer period of time is required for synchronization. 2. An increase in the number of individual objects requires an increase in the range of concepts and the amount of time in order to achieve an in depth synchronization. 3. Initial concept values which randomly effect synchronization critical point conditions are not obvious in a mathematically incorrect graph. In a closer look, when we increased the synchronization to n≦400 and the number of times to t-->100,000 we discovered:1. Using the function G(x) we hoped the results from the graph after apply the function and correction able to overlap and test with “Scaling and Universality in Transition to Synchronous Chaos with Local-Global Interactions”, but the part which overlapped the measurements was not identical: 2. We can use the significance of the critical point and the Interactive Process to find the approximate value of the critical value up to 4 digits following the decimal point. 3. We can also use the approximate value to find out the range for the simultaneous conditions and the various points on the system itself, as well as obtain a negative correlation between them, and then it can be similarly expressed with using a curve. A computer can calculate values with this kind of enumerating method, even without any special resolution capabilities to quickly obtain large amounts of approximate values of simultaneous conditions, this is especially true when calculating unfamiliar systems. 日常生活中,物件與物件的接觸,彼此會互相影響,有些原本雜亂的系統再經過充裕時間的互相修正後,最後竟能達成同步(例如:鳥群、魚群遷徙的速度、市場價格、行軍步伐…),有些則不能。因此,我們試著利用描述同步系統的模型,觀察系統同步的過程,並且找出同步的條件。由連結的觀點,我們將Coupled map lattices with global coupling 和Coupled map lattices with intermediate-range 模型的優點整合成Synchronization mode 去模擬同步系統。我們先用小系統(n≦50)得到能印證連結觀點的結果:(一)、系統越雜亂,就需要稍長的時間同步;(二)、個體數越多時,各點需要更大範圍的點數去影響於每單位時間內以及更深的影響才能同步;(三)、起始值隨機影響同步臨界條件並不明顯,在誤差範圍內。更進一步,我們將系統推向n≦400 點,t→100,000 次,我們發現:(一)、在”G(x)”我們希望能將圖形經過函數修正之後能疊和,驗證”Scaling and Universality In Transition to Synchronous Chaos with Local-Global Interactions ”中的結果,但只有部分疊和,尺度不相同;(二)、可以直接利用臨界點的意義用十分逼近法求出臨界值的近似值到小數後四位;(三)、我們用近似值也能發現同步條件與系統各點本身可跳躍的數值範圍是負相關,可用曲線去近似。這種窮舉方式,交由電腦運算,不需要特別的解析能力就能夠快速且大量求得同步條件的近似值,尤其在運算不熟悉的系統時。


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