自發性同步：透過雙層振盪器探討群體動力學

Abstract

在音樂廳中，一位聽眾的拍手行為是由拍手那位聽眾的意志，來決定拍手動作的頻率與音量；但聽眾全體那同步化的拍手行為卻不是。而「聽眾全體同步地拍手」的行為，在大自然中被稱為「自發性同步」。自發性同步並非人類與動物的專利，而是在一個系統在受到局部效應後，如何讓系統整體逐步因應局部效應而變化的演示。 在我們的模擬中，我們會展示一個二層共振子系統在其中一層有類似水波那樣的點狀擾動時，對另外一層、甚至整個系統運動的影響。然而，觀察波動對一個完全沒有雜質的系統其實沒有什麼很大的意義。對此，我們會引入三種「雜質粒子」，障礙物、放大器與反射器，以觀察三種雜質粒子如何讓系統產生對應的變化、甚至如何對系統的自發性同步產生什麼影響。

In an auditorium, the applause of one audience member is driven by individual thought, but synchronized applause from all audience members is not. In nature, a phenomenon similar to synchronized applause is Spontaneous Synchronization (Sync). Sync is not unique to humans or animals but demonstrates how a local effect can cause an entire system to change in an orderly manner. In our simulation, we demonstrate Sync in a two-layer oscillator system, showing how an initial point perturbation in one of the layers leads to the simultaneous motion of both layers. However, it's overly simplistic to study how a wave influences an oscillator system without any objects. To gain deeper insights, we introduce three types of objects—blocks, amplifiers, and reflectors—into the system to observe how replacing some particles with these objects alters the system's behavior. In our simulation, we will examine how these objects—blocks, amplifiers, and reflectors—impact the oscillator system and its ability to achieve synchronization.