Periods and Amplitudes of Oscillations in Coupled Systems

• Main Authors: Chen, Kuan-Wei, 陳冠維
• Other Authors: Shih, Chih-Wen
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/85462070598103360844

碩士 === 國立交通大學 === 應用數學系數學建模與科學計算碩士班 === 101 === In this thesis, we study the periods and amplitudes in coupled oscillations. The study is motivated by some interesting investigations in mathematical models on biological clocks. Herein, we couple two oscillators, and use the Hopf bifurcation theorem to show that the coupled oscillation is sustained. We observe the relation between the collective period and the isolated individual periods. We also study the amplitudes of oscillations in coupled systems. In particular, we discuss the oscillations in three-cell feed-forward by Golubitsky and collaborators, where synchrony-breaking Hopf bifurcations may happen in some feed-forward network, and amplify the periodic signals. We summarize these results, and extend the study to the variation of amplitudes in a four-cell feed-forward chain. Finally, we give some numerical simulation to illustrate our results.