Novel Codimension-two Bifurcation in a Coupled Duffing System with Twisted frequency-response Curves

具彎曲頻率響應曲線偶合杜飛系統之新共維度二分歧現象

蕭永嘉(Yung-Chia Hsiao) ； 賴廷裕(Ting-Yu Lai)

《明道學術論壇》 4卷1期 (2008/06) Pp. 13-28

https://doi.org/10.6953/MJ.200806.0013

摘要

本論文發現在某些參數下具彎曲頻率響應曲線之偶合杜飛系統在某些參數下產生新共維度二分歧現象。此現象由週期加倍分歧、鞍點－節點分歧、霍伯夫分歧及混沌運動所組成。週期運動之鞍點－節點分歧線與週期加倍分歧線相交於一共維度二分歧點，而次簡協運動之霍伯夫分歧線與此點相交後消失並同時產生混沌運動。為分析上述現象，文中應用發射法求得系統之週期解及次簡諧解，而頻譜響應圖則以簡諧平衡法求之。其穩定性分析則利用Floquet理論求得。

關鍵字

分歧 ； 共維度二 ； 混沌 ； 杜飛系統 ； 次簡諧運動

並列摘要

This paper studied a novel codimension-two bifurcation combined by chaos and bifurcations of periodic orbits of period-1 and subharmonic orbits of period-2 in a coupled Duffing system with twisted frequency-response curves. A bifurcation line constructed by the saddle-node bifurcations of periodic orbits of period-1 tangentially intersects a bifurcation line constructed by the period doubling bifurcations of periodic orbits of period-1 at a codimension-two bifurcation point. Meanwhile, a Hopf bifurcation line constructed by the Hopf bifurcations of subharmonic orbits of period-2 merges into the codimension-two bifurcation point and then disappears. In this moment, chaos is generated simultaneously. 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.

並列關鍵字

bifurcation ； codimension-two ； chaos ； Duffing System ； subharmonic orbit