duffing method 中文意思是什麼

duffing method 解釋
杜芬法
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  1. Thirdly, we consider the n - dimensional duffing type equation with damping term. by virtue of homeomorphism, extension and fixed point method, we discuss the existence of periodic solution under the nonresonance condition

    再次，我們考慮n維的帶有阻尼項的duffing型方程，運用同胚延拓及不動點方法，討論了非共振條件下周期解的存在性問題。
  2. Then the characteristic and estimation approaches of two important time variant parameter ( tvp ) and state dependent parameter ( sdp ) models are presented and the efficiency of the dbm method is illustrated by three examples based on the analysis of duffing equations, lorenz equations and time - variant equation, in contrast with other methods

    本文首先總結了dbm在常規黑箱辨識演算法中的基本框架和兩類重要模型?時變參數（ timevariantparameter ， tvp ）模型和狀態依存參數（ statedependentparameter ， sdp ）模型的特點及其估計演算法。
  3. Secondly, the effectiveness and limitation of the classical perturbation, such as the method of multiple scales and the poincare - lindstedt method, are discussed in detail through a duffing oscillator with delayed velocity feedback. it is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders. an ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution

    其次，以一具有時滯速度反饋的duffing系統為例，研究了經典攝動法如多尺度法， poincar - lindstedt法等在求解時滯微分方程級數解時的適用性和局限性問題，指出利用這些方法只能有效求得系統的前兩階近似解，而在求系統的三次以上近似解時會出現矛盾或二義性。
  4. Simulation results of a duffing forced - oscillation system confirm that the effect of the fuzzy approximation error on the tracking error can be attenuated efficiently by the proposed method

    強迫震?系統的模擬結果確定在模糊近似誤差的影響下，追蹤誤差能被有效的衰減。
  5. Based on chaos critical state detection method, two approaches are used : one is that making a pretreatment on dsss signal to take out the period information of the signal. the other is that starting from the analysis of the sensitivity of duffing system to ambi - polar square wave modulated by sine signal, the

    通過兩種途徑:對信號進行預處理，提取出其中的周期信息，轉化為單頻信號檢測;從研究duffing振子對方波調制信號的敏感性出發，全面分析其中的間歇混沌現象，實現信噪比- 20db以下dsss信號的檢測。
  6. At last, the stability switches of equilibrium and the global diagrams of bifurcation for a duffing oscillator with both delayed velocity feedback and delayed displacement feedback are studied by using the similar method as above

    最後，研究了時滯位移反饋與時滯速度反饋聯合作用下duffing系統的平衡點的穩定性切換及全局hopf分叉。
  7. Afterwards, a duffing system with delayed displacement feedback is studied by the method of multiple scales and other numerical methods. the uniform formulas for computing the critical values of time delay are given and the global diagrams of bifurcation for the periodic solutions with respect to the time delay are obtained under different parametric combinations. it is shown that the hopf bifurcation and the saddle - node bifurcation are the only two types of bifurcation observed in such a system

    接下來用多尺度法及數值方法研究了一具有時滯位移反饋的duffing系統的動力學，得到了不同參數下系統平衡點發生穩定性切換時的臨界時滯計算公式及關于時滯的大范圍hopf分叉圖，並發現saddle - node分叉及hopf分叉是系統出現周期運動的兩個主要的來源。
  8. In the second part, we try to apply orthogonal polynomial approximations to the dynamical response problem of the duffing equation with random parameters under harmonic excitations. we first reduce the random duffing system into its non - linear deterministic equivalent one. then, using numerical method, we study the elementary non - linear phenomena in the system, such as saddle - node bifurcation, symmetry break bifurcation, phenomena in the system, such as saddle - node bifurcation, symmetry break bifurcation, period - doubling bifurcation and chaos

    本文第二部分嘗試將正交多項式逼近方法應用於隨機duffing系統，提出與之等價的確定性非線性系統的新概念，並用數值方法對該系統在諧和激勵下的鞍結分叉、對稱破裂分叉、倍周期分叉、和混沌等各種基本非線性響應進行了初步探討。
  9. 3. making a deep research on weak sinusoid signal detection using duffing oscillators and combining chaos critical state detection method with general detection methods, this dissertation realizes weak sinusoid signal detection below - 50db snr. furthermore, starting from the analysis of the intermittent chaotic motion occurring in the detecting process, an array of duffing oscillators are used to estimate the frequency of weak sinusoid signals accurately

    （ 3 ）全面深入地研究了duffing振子用於微弱正弦信號檢測的機理，並把混沌臨界狀態檢測法和傳統檢測方法相結合，實現- 50db以下超低信噪比的微弱正弦信號檢測;建立了混沌振子陣列，實現低信噪比下正弦信號頻率的估計。
  10. Two illustrative examples, a duffing oscillator subject to a harmonic parametric control and a driven murali - lakshmanan - chua ( mlc ) circuit imposed with a weak harmonic control, are presented here to show that the random phase plays a decisive role for control function. the method for computing the top lyapunov exponent is based on khasminskii ' s formulation for linearized systems. then, the obtained results are further verified by the poincare map analysis on dynamical behavior of the system, such as stability, bifurcation and chaos

    通過兩個實例，即一類參激激勵作用下的duffing系統和一類murali - lakshmanan - chua （ mlc ）電路，考察隨機相位在非反饋混沌控制中的影響與作用，利用最大lyapunov指數和poincare截面分析法證實了隨機相位確實可以用來調節系統的混沌行為，即一個小的隨機相位的擾動可能導致系統從有序轉變為無序，也可能使得系統從無序轉變為有序。
  11. Many studies have been carried out on the system described by duffing equation ( 2 ), but very few on equation ( 1 ) by using the analytical method

    前人對duffing方程（ 2 ）描述的系統進行了許多研究，但很少見到用解析方法研究方程（ 1 ） 。
  12. The research work on the chaos is carried out in chapter 5. the properties of chaos sensitively dependent on the initial conditions and the perturbations are proved and a method of controlling chaos of duffing oscillator is investigated as well. in chapter 6, the bifurcation and chaos of continuous nonlinear systems are researched

    第五章用正規攝動法給出了一維非線性微分方程的通解，並以此為基礎解析地證明了混沌運動對初值的敏感依賴性和對擾動的敏感依賴性，並以杜芬振子為例子以驗證，研究了杜芬振子的混沌運動控制的多諧擾動法。
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