三個倉本模型的振盪粒子在時間延遲效果下頻率同步的全局收斂性

Abstract

本論文研究了在時間延遲下之倉本模型的集體同步行為。 倉本模型已被大規模用來研究耦合振盪粒子的同步行為。 其成果被應用在諸如物理學、生物學以及網絡等廣泛的科學學科中。經典的倉本模型假定振盪粒子之間的相互作用是瞬時的。 但是，在現實世界的系統中，粒子之間的交互作用並不是瞬時的，因為我們必須考慮信號傳播時間和決策過程。 因此，考慮時間延遲模型是很自然的。 例如，在神經網絡以及鐳射和微波振盪器的陣列中，突觸、樹突和傳播延遲都是必須被考慮的。 本論文的主要結論是在自然頻率相同的情況下，三個倉本模型的振盪粒子在時間延遲效果下頻率同步的全局收斂性。

The thesis studies the collective behavior of synchrony for the full-delay Kuramoto model. The Kuramoto model has been studied for the synchronization behavior of coupled oscillators. It is also applied in widely scientific disciplines such as physics, biology and networks etc. The classical Kuramoto model assumes that the interactions between oscillators are instantaneous. However, in the real-world systems, the interactions between the elements are not instantaneous since we have to take signal propagation time and decision making process into consideration. Hence it is natural to consider the time delay model. For examples, in the neural networks, and also in the arrays of lasers and microwave oscillators, the synaptic, dendritic, and propagation delays must be taken into account. The main conclusion of this thesis is the global convergence of frequency synchronization for three Kuramoto oscillators under time-delay effect in the identical case.