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題名 | 達夫動力系統承受雙頻率激振的週期響應與混沌運動之分析=Periodic and Chaotic Responses the Duffing System with Two External Excitations |
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作者 | 簡守謙; Jen, Shoou-chian; |
期刊 | 德霖學報 |
出版日期 | 20110600 |
卷期 | 25 2011.06[民100.06] |
頁次 | 頁85-95 |
分類號 | 446.11 |
語文 | chi |
關鍵詞 | Melnikov's方法; 分歧圖; 雙頻率激振; 混沌; Melnikov's method; Bifurcation; Two external excitations; Chaos; |
中文摘要 | 探討與分析達夫(Duffing)動力系統受雙頻率激振的分歧現象與混沌運動。首先以數值分析,在相同吸 子盆地(Basins of attraction),穩態解的起始值是以基本週期交替出現之特性。其次以Melnikov 解析方 法,求取達夫動力受雙頻率激振時,週期運動與混沌響應的臨界參數值。取多個初始條件之分歧圖,能 分辨頻率互鎖與類週期之響應,有出現週期三響應,並呈現週期倍增至混沌;配合以相圖、頻譜圖、Poincarè 切面圖、響應時序圖和Lyapunov 指數,證明分歧圖在參數變化之穩態響應之型態。 |
英文摘要 | Periodic and chaotic responses the Duffing system with two external excitations are investigated. First, the boundary of periodic and chaotic motion under the periodic perturbation is determined by using Melnikov’s method. Second, using numerical integration, based on 4th order Runge-Kutta method is used to simulating Duffing system for various initial conditions and parameters. As bifurcation diagrams are plotted, frequency-locked oscillations with period-3 motions and cascades of period-doubling to chaos are found. Numerical simulations including homoclinic bifurcation surfaces, bifurcation diagrams, Poincaré maps, phase portraits, response waveforms, frequency spectra and maximum Lyapunov exponents are given to illustrate the theoretical analysis. |
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