The complex bifurcations of a coupled Duffing system

• Main Authors: Wei-Cing Li, 李威慶
• Other Authors: Yung-Chia Hsiao
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/61696647106063177316

碩士 === 明道大學 === 材料科學與工程學系碩士班 === 97 === Duffing equation is one of the common nonlinear differential equations with a harmonic driving force and cubic nonlinearity. Many investigations described that the secondary responses coexist with the primary responses. Hsiao and Tung observed that the subharmonic orbits of the secondary responses separate from the subharmonic orbits of the primary responses via the coalescence of two saddle-node bifurcations points of the subhramonic orbits in a couple Duffing system. This thesis observed another separation of the secondary responses and the primary responses. The subharmonic orbits of the secondary responses separate from the primary responses via the coalescence of two period doubling bifurcations points of the periodic orbits. To analyze the phenomenon, the periodic orbits and the subharmonic orbits are detected by using the shooting method and the frequency responses are obtained through the harmonic balance method. Besides, the stability of the obtained orbits is performed using the Floquet theory.