saddle focus 中文意思是什麼
saddle focus
解釋
鞍式焦點-
The yen to go back to basics means consumers will shun garish status symbols to focus on core values like quality. with firms firing staff and stock markets tumbling, it may seem tasteless to flout a new 0 dior saddle " bag, but buying a cashmere sweater from donna karan qualifies as an investment
在即將過去的一年中各大公司紛紛裁員，股市狂跌，在如此不景氣的經濟環境下，與其花600美元買一個dior的掛包在人前炫耀，還不如去買一個donna karan牌的開司米羊毛衫來的實惠。 -
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。 -
The first 3 focus quantities and the first 3 saddle quantities are derived simply and quickly with the formulas for real planar quadratic systems
利用這一公式我們極其簡捷地推導出二次系統的前三個焦點量和鞍點量公式。 -
Especially, when the isocline of x is monotone decreasing in 0 < x < 1, the svstem has no limit cycle and is globally stable ; next, we construct a saddle bifurcation at the boundary equilibrium and a degenerated bogdanov - takens bifurcation at the interior equilibrium by choosing appropriate parameter values in the following two sections, where our work are based on the theory of central manifolds and normal torms. we prove that is a codimention 3 focus - type equilibrium. system ( 6. 1 ) will have two limit cycles at some appropriate bifurcation parameter values, and have homoclinic or double - homoclinic orbits at some other appropriate bifurcation parameter values ; at last, we study the qualitative properties of the system at infinite in the poincare sphere
因為系統在（ 0 ， 0 ）點處沒有定義，這給研究其在（ 0 ， 0 ）附近的動力學性質帶來了困難，我們應用文獻[ 17 ]中關于研究非線性方程奇點的系列理論和方法，圓滿解決了這一問題，給出了第一象限內當t +或t -時，在全參數狀態下系統的軌線趨于（ 0 ， 0 ）點的所有可能情況，其相圖也得以描繪；並且，系統不存在極限環的幾個充分條件我們也予以列出，當x的等傾線在0 x 1范圍內遞減時，系統不存在極限環，全局漸近穩定；然後，我們以中心流形定理和正規型方法為主要工具，巧妙選擇參數，分別構造了一個余維2的鞍點分岔和一個余維3退化bogdanov - takens分岔，證明了平衡點是余維3的焦點型平衡點，存在參數， m ，的值使得系統（ 6 . 1 ）有兩個極限環，還存在參數， m ，的另外值使得系統（ 6 . 1 ）有同宿軌或雙同宿軌。 -
So far, there is no effective method for the computation of focus quantities and saddle quantities. compared with the work of other authors, complex nonlinear integrating operation and solving multivariate linear equations are avoided in computation, which are necessary in more usual approaches. the calculation and simplification of focus quantities can be readily done with these formulas and computer symbol operation systems
焦點量與鞍點量的計算至今尚無有效的方法，對比以往其他作者的工作，在計算方法上，我們避免了通常計算焦點量需要的非線性積分運算和求解多元方程組，使得焦點量極易在計算機上應用計算機符號運算系統進行快速計算和化簡。 -
The global bifurcation analysis of the nonlinear nonplanar cantilever is given by a global perturbation method developed by kovacic and wiggins. it is found that the nonlinear nonplanar cantilever can undergo the hopf bifurcation, heteroclinic bifurcations and silnikov - type homoclinic orbit to saddle focus, which means that the nonlinear nonplanar cantilever can give rise to the chaotic motion in the sense of smale horseshoes
利用kovacic和wiggins的全局攝動法對非線性非平面運動懸臂梁進行了全局動力學分析，發現系統存在hopf分叉和異宿分叉，並證明系統有silnikov型鞍焦點型同宿軌道，可以產生smale馬蹄意義下的混沌。 -
In chapter 2, by studying the computation of the quantities of singular point of the original of the following complex autonomous polynomial differential system two linear recursion formulas for the computation of quantities of singular point of system ( 1 ) are obtained. applicable formulas are presented unitedly for the computation of focus quantities and saddle quantities, which play an important role in center - focus determination and bifurcation of limit cycles in real planar polynomial differential systems
在第二章，我們研究平面多項式復自治微分系統原點的奇點量計算，得到了奇點量計算的線性代數遞推公式，統一地給出了在實平面多項式微分系統的中心焦點判定與極限環分支中有著極為重要意義的焦點量與鞍點量的易於應用的計算公式。
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