發(fā)布時間：2018-11-15 17:38

【摘要】：爆發(fā)式同步現(xiàn)象指的是復(fù)雜網(wǎng)絡(luò)上的振子,隨著耦合強(qiáng)度的增加,從混亂狀態(tài)開始,經(jīng)歷一個不連續(xù)的、伴隨著磁滯區(qū)的一級相變,變化到同步狀態(tài)的過程。自2011年西班牙小組發(fā)表了 Kuramoto模型在Scale-Free網(wǎng)上的爆發(fā)式同步以來,該領(lǐng)域迅速成為了熱點(diǎn),得到了廣泛的關(guān)注。隨后胡鑫、張希昀等人,在前人的基礎(chǔ)上提出了以振子本征頻率作為耦合權(quán)重的新的廣義Kuramoto模型,取得了一系列的研究成果�？紤]到簡化理論計算等原因,之前所研究的頻率權(quán)重模型,其本征頻率都取為對稱的分布,而頻率分布非對稱的情形并未得到研究。從這一點(diǎn)出發(fā),本文研究了頻率權(quán)重模型在典型的非對稱頻率分布下的同步化行為。通過數(shù)值模擬和理論分析,我們得到了以下主要結(jié)果:1.在多種非對稱頻率分布下,頻率權(quán)重Kuramoto模型都能表現(xiàn)出爆發(fā)式同步現(xiàn)象,并且隨著系統(tǒng)非對稱性的增強(qiáng),系統(tǒng)會由一級相變逐步過渡到二級相變;2.在非對稱洛倫茲分布和非對稱三角分布中,發(fā)現(xiàn)并刻畫了一類新的協(xié)同態(tài),即具有陣發(fā)特性的Bellarophon態(tài)。本文的結(jié)果能幫助我們更加全面地理解耦合相振子系統(tǒng)中的爆發(fā)式同步。
[Abstract]:The explosive synchronization phenomenon refers to the oscillator in a complex network. With the increase of coupling intensity, it goes through a discontinuous first order phase transition along with the hysteresis region and changes to the synchronous state with the increase of the coupling strength. Since the Spanish team published the explosive synchronization of the Kuramoto model on Scale-Free in 2011, the field has quickly become a hot spot and received wide attention. Subsequently, Hu Xin, Zhang Xiyun and others put forward a new generalized Kuramoto model with the eigenfrequency of oscillator as coupling weight on the basis of predecessors, and obtained a series of research results. Considering the simplified theoretical calculation and other reasons, the eigenfrequencies of the previously studied frequency weighting model are all symmetric distribution, but the asymmetric frequency distribution is not studied. From this point of view, the synchronization behavior of the frequency weight model under the typical asymmetric frequency distribution is studied. By numerical simulation and theoretical analysis, we get the following main results: 1. Under a variety of asymmetric frequency distributions, the frequency weighted Kuramoto model can exhibit explosive synchronization phenomenon, and with the increase of the system asymmetry, the system will gradually transition from the first-order phase transition to the second-order phase transition; 2. In the asymmetric Lorentz distribution and the asymmetric triangular distribution, we find and characterize a new class of cooperative states, that is, the Bellarophon states with the property of matrix. The results in this paper can help us to understand the burst synchronization in the coupled phase oscillator system more comprehensively.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5

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本文編號：2333986