Numerical Investigations of Synchronization of Locally Coupled Oscillators in One Dimension

• Main Authors: Kuo, Huan-Yu, 郭桓玉
• Other Authors: 吳國安
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/34059351076372550080

碩士 === 國立清華大學 === 物理系 === 102 === The focus of our research is to understand the synchronization phenomena among a finite size network of oscillators with power-law coupling in an one dimensional chain. Renormalized Kuramoto model with periodic boundary conditions and Cauchy distribution of natural frequency are used in this thesis. In locally coupled system the oscillator couples to its local mean field rather than the mean field in globally coupling case. In order to analyze synchronization phenomenon of locally coupled oscillators, we develop a measurement tool, ξ, as the difference of local order parameter between any two nearest neighbours. The variation contains the information of system size N and the decay rate of coupling α, and its value shows how the local mean field deviates from the mean field. As variation decreases to zero, the phase coherence is independent of the local couplings and system size, which means that the locally coupled system at low variation is a globally coupled system. In addition, the phase coherence becomes oscillatory with time as the variation ξ becomes larger. We find that the occurrence of the oscillatory state is due to the splitting of oscillators into multiple groups; oscillators in the same group remain synchronized. The formation of oscillatory state is shown to be sensitive to initial spatial arrangements of natural frequency of oscillators. We propose a systematic approach to predict the occurrence condition of oscillatory states.