hopf bifurcation 中文意思是什麼
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An analysis of hopf bifurcation in a chaotic system
一個混沌系統的霍普夫分叉分析 -
Also according to the basic solution matrix, hopf bifurcation of is investigated by creating subsequence functions, the measure of which differs from that of autonomous system. in the paper i apply myself to seek out a new idea to investigating heteronymous system that is no longer stickled in autonomous system
同樣以這個基本解方陣為依據，本文接著研究二維周期系統的hopf分支，所用方法是構造后繼函數法，但在具體構造方法上，與自治系統的hopf分支不同，本文致力於探索一種不再拘泥於自治系統的，研究非自治系統hopf分支的新思路。 -
In this paper we study the single - species chemostat model with time dilay. based on [ 8 ], we analyze the hopf bifurcation of the system which take the diluton as a parameter, and we obtain that under the conditon of the existence of positive equilibrium and if the dilution is too big or too small, the system will appear hopf bifurcation
在文[ 8 ]的基礎上，以模型中的流量為參數進行了hopf分支分析。得出了在正平衡點存在的條件下，當流量較大或較小時，系統的正平衡點附近會產生hopf分支，並應用中心流形和規范形理論給出了分支方向及分支周期解穩定性的計算公式。 -
The bifurcation analysis of the model depending on all parameter indication that it exhibits numerous kinds of bifurcation phenomena, including the saddle - node bifurcation, the supercritical and subcritical hopf bifurcation, and the lioinoclinic bifurcation. in the generic case, the model has the bifurcation of cusp type ol ' codimension 2 ( i. e. bogdanov - taken bifurcation ) but for some specific parameter values it has a multiple focus of multiplicity at least 2. and, we give the global analysis
本文考慮具非單調功能反應函數的捕食者?食餌系統，討論了系統的bogdanov - taken分支，給出了不同種類的分支現象，包括鞍-結點分支，上臨界與下臨界hopf分支，和同宿軌分支，並討論了無窮遠點的定性分析，給出了全局結構。 -
Application research of hopf bifurcation theorem in nonlinear oscillation circuits
分叉定理在非線性振蕩電路中的應用 -
Numerical approximation of hopf bifurcation for delay logistic differential equation
分支參數值的數值逼近 -
Moreover, with the method of emerging hopf bifurcation of the system, the analytic conditions that the low - dimension continuous autonomous chaotic systems controlled by the project are given in theory. applying the conclusions we got to the practical systems, the method is shown by the theoretical description and numerical calculation that it is effective
其次，從實際應用出發，提出了一種增強型的延遲變量反饋控制方案，同樣利用分析延遲系統產生hopf分支條件的方法，也給出了當用這種方案控制低維連續自治混沌系統時，在達到控制目標的條件下，控制參數間的一般解析關系。 -
Finally, this paper set up the substitute model between the new technology and the old one and studied characteristic of the diffusion system applied system dynamic method such as the stable points and phase portrait and hopf bifurcation and limit cycle of it. then studied the probability distribution function of them, and the probabilistic equation of this system
最後建立了四川大學碩士畢業論文創新技術和舊技術的技術更替模型，並運用系統動力學的方法分析了擴散系統在其不動點附近的變化特徵和相圖以及改進系統的hopf分支、極限環等性質，討論了新舊技術的概率分佈，並且將動力學方程轉化為概率方程進行分析。 -
We use the poincare - andronov - hopf bifurcation theorem to prove that there is an invariant curve in the center manifold when the coupling coefficient e is small enough
利用poincar - andronov - hopf分支定理證明系統有弱空間耦合時在中心流形上存在不變圈。 -
The dynamics behaviors of the flexible jeffcott rotor system supported by unsteady short dynamic bearing are investigated. based on nonlinear unsteady - state dynamic n - oil film force model described by three functions the local stability of the periodic solutions with the controlling parameters, rotational speed ratio, imbalance amount, damping ratio and viscidity, are predicted by using the floquet multiplier. it is found that the period doubling bifurcation is caused by a certain imbalance amount and the hopf bifurcation is created by the lost stability of the oil - film
研究了非穩態動載短軸承支撐的jeffcott柔性轉子系統的動力特性，基於可用三個函數表示動態油膜的非穩態非線性油膜力模型，將轉速比、不平衡量、阻尼比、粘度作為控制參數，利用floquet乘子預測周期解的局部穩定性，發現倍周期分叉是由一定量的不平衡引起的，而hopf分叉是由油膜失穩造成的。 -
At the point of co = g > c, it is the hopf bifurcation that the rotor orbit of shaft centerline is the periodic whirl of small amplitude. the method is suitable for the multi - freedom system
數值求解系統動力學方程，在_ c處，轉子軸心軌跡為極小幅值的周期渦動，此為hopf分岔，分叉后，系統運動為擬周期運動。 -
In the second section, we study the multiplicity of weak focus in system ( 1 ) when b = 0, then system ( 1 ) becomes : in [ 7 ], the authors show that system ( 2 ) has rich global dynamics depending on all parameters, including a weak focus with multiplicity at least 2, but the authors did n ' t calculate the multiplicity. in the second section of this article, we calculate the order of the weak focus with formative series method and mathematica 4. 0, and show that the order of the weak focus is two for some parameters. we also get the stability, then by hopf bifurcation theorem, we show that system ( 2 ) has at least two limit cycles for some parameters
而且我們選擇了系統的原參數中的二個作為分支參數，可以使系統（ 1 ）進行bogdanov - takens余維2普適開折，從而證明系統（ 1 ）同宿軌的存在性。第二部分我們討論系統（ 1 ）當b = 0時細焦點的階數。當b = 0時，系統（ 1 ）為一文7對系統p ）進行了全參數分析得到系統）豐富的全局動力學性質，但當參數取某些值時系統間出現了階數大於或等於2的細焦點，文沒有計算該細焦點的階數。 -
The effect of track stiffness and track damping on high - speed train hopf bifurcation speed is discussed. the difference of the lateral stability between vehicle and train under the same track conditions is given. during the research course, the effect of bogie suspension parameters, track parameters, lateral link stiffness and lateral link damping between cars on train ( vehicle ) hopf bifurcation speed are also educed
在研究過程中，既研究了車輛系統懸掛參數對列車（車輛） hopf分叉速度的影響，也研究了軌道參數對列車（車輛）系統hopf分又速度的影響，同時還研究了車間橫向連接剛度導和橫向連接阻尼系數對列車系統運動穩定性的影響。 -
In this paper periodically perturbed hopf bifurcation to lienard equation with limited time delay is sdudied in detail. that is, the influence of small periodic perturbations on system exhibiting hopf bifurcation is sdudied. in particular, the excitation frequency and the critical natural frequency of hopf bifurcation in the cases of harmonic resonance. subharmonic resonance, ultraharmonic resonance, and ultrasubharmonic resonance is discussed. it is shown that in some parameter regions the sestyms exhibit harmonic solution bifurcation, subharmonic solution bifurcation, ultraharmonic solution bifurcation, ultrasubharmonic solution bifurcation and quasi - periodic solution
本文詳細研究了具有限時滯li nard方程的周期擾動hopf分支，即在該系統經歷hopf分支時，研究小周期擾動對系統的影響，特別是討論了擾動頻率與hopf分支周期解的固有頻率在共振、次調和共振、超調和共振、超次調和共振的情形。 -
By analyzing the eigenvalues of linear variation equations, some algebraic criteria for the absolute stability ( independent of the delays ) are established for two special 3 - dimensional systems. also, the sufficient conditions under which the systems hold a hopf bifurcation are obtained, which are easy to verify
我們通過分析特徵方程的特徵根，獲得了平衡點絕對穩定的代數判據，同時得到系統存在hopf分支的充分性條件，這些判據在實際中易於驗證。 -
By means of the precise integration method with lagrangian interpolation the trajectory of the shaft center, the poincare mapping and the bifurcation graphs are numerically given. the results predicted by the floquet theory are checked and the long - term dynamic behavior of the system is predicted. it is shown that the system has rich nonlinear behaviors at some m combination of the four parameters, for examples, multi - frequency subharmonic resonance, as well as chaos phenomenon from doubling bifurcation and twice hopf bifurcation
通過lagrange插值精細積分法數值給出系統的軸心軌跡圖、 poincar映射圖、分叉圖，檢驗floquet理論預測結果並預測系統的長期性態，顯示系統在四個參數組合的某些范圍內具有豐富的非線性特性，還存在多形式次諧波解，以及由倍周期分叉、二次hopf分叉通往混沌的現象。 -
Lastly, we apply the formulae about the quality of ilopf bifurcation we have obtained to a concrete example, calculating the stability of periodic solution, the direction of hopf bifurcation and the expression of bifurcated periodic solution
最後，我們將已經得到的判斷hopf分支性質的計算公式應用到一個具體的例子上，求出這個方程的hopf分支周期解的穩定性，分支方向及分支周期解的近似表達式。 -
In addition to the familiar period doubling bifurcation scenario leading to chaos, a quasiperiodic route to chaos is also observed which occurs through an initial hopf bifurcation. the current chaos control methods are compared, the stabilization of unstable periodic orbits of this chaotic system is achieved by continuous feedback control method, the specially designed external oscillator which used as target motion orbit in continuous feedback control method is obtained directly from ihb method
對現有的混沌控制方法的優缺點進行了比較，利用混沌控制理論中的連續變量反饋控制方法，實現了系統混沌吸引子內部的不穩定周期軌道的穩定化，對齒輪傳動系統進行了有效的混沌控制，並對連續變量反饋方法的結果進行了分析，包括噪聲的影響和方法的改進。 -
The main research work involves : ( 1 ) based on first order ode ( ordinary differential equation ) approximation theory and hopf bifurcation theory, the nonlinear motion stability of the train is studied emphatically
本文所做的主要工作有： （ 1 ）基於常微分方程的一次近似理論和hopf分叉理論，重點研究了列車（車輛）系統的非線性運動穩定性。 -
The first part of this paper ( chapters 2 and 3 ) discusses the stability and hopf bifurcation for two classes of retarded differential difference systems
本文的第一部分（第二章、第三章）就是討論兩類特殊形式的滯后型微分差分系統的穩定性和hopf分支的存在性
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