頻率變換與脈波耦合複雜網路之同步化研究

在這自然界中，有很多同步的過程以及現象，例如螢火蟲的同步閃爍、心律細胞的同步、人群在鼓掌時的聲響、以及化學反應的震盪。這些現象在各個不同的個體間，在不同狀況，是如何連結、傳達資訊以產生同步，是一個有趣且令人注目的研究課題。本論文透過使用無線感測器，以ZigBee傳遞資訊，並利用Peskin模型模擬螢火蟲閃爍的情形。接著改良Peskin模型的耦合方式，探討不同的連結方式下的同步化現象。除此之外，也特別去觀察及分析，不同於以往耦合所出現的現象。吾人認為，傳統的耦合方式並不合乎常理，像人群鼓掌的複雜網路系統，在初始至同步時的頻率並不是固定的值，應該是隨著節點自身的狀態以及收到的訊號來做調整。使用此種耦合模式，頻率及狀態都要相等的狀況下，才能稱為同步。對同步過程中，頻率及狀態的變化情形，以及如何達到完全同步進行討論。我們也發現使用線性的模型，也能到達同步的效果。

關鍵字

複雜網路；同步；脈波耦合

並列摘要

In this natural world, there are many processes and phenomena of synchronization. For examples, synchronous flash of fireflies, beats of pacemaker cells in the heart, clapping sound of crowd, and oscillating chemical reactions. The study of understanding the mechanism for those synchronization phenomena under different conditions is an interesting and exciting issue. This thesis tries to simulate the flash of fireflies by using Peskin model, and to build up a wireless-sensor network to mimic the synchronous flash by taking ZigBee technology to communicating flashing signals among coupled sensors. Beside, the deep discussion on how to improve coupling effect with respect to various connection topologies and coupling mechanisms among a group of oscillators is well carried out. Almost work in the literature only consider to increase an amount of oscillators when the oscillator is triggered. However, we think the typical updation of phase is insufficient to reflect the synchronization phenomena coming from a real world. One of the observations is, for example, the frequencies of crowd clapping are not all the same value from the beginning till to synchronization. This motivates us to consider the effect due to variable synchronizing frequency. We found that under many types of coupling topologies, a group of many oscillators will eventually reach synchronization under a modified mechanism called as the updation of both phase and frequency.

並列關鍵字

Complex Network ； Synchronization ； Pulse-Coupled

參考文獻

[10] Y.-C. Hu, Synchronization of Complex Networks with Pulse-Coupled Integrate-and-Fire Oscillators, Master Thesis, National Taipei University of Technology, Taipei, Taiwan, 2009.

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[4] A. L. Barabási and R. Albert, “Emergence of Scaling in Random Networks”, Science, vol. 286, pp. 509-512, 2001.

[5] R. Albert and A.-L. Barabási, “Statistical mechanics of complex networks”, Review of Modern Physis, vol. 74, 2002, pp. 47-97.

[6] M. E. J. Newman, “The structure and function of complex networks”, SIAM Reviews, vol. 45(2), 2003, pp. 167-256.

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頻率變換與脈波耦合複雜網路之同步化研究

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