1) singularly perturbed
奇异扰动
1.
By means of inverse proof, it is proved that u ε=m 1p-1 ε ω ε exists at least two local maximum points for a singularly perturbed Neumann problem on a symmeric domain.
利用反证法证明 ,在奇异扰动Neumann问题上 ,uε =mε1p- 2 wε 至少有两个局部最大值点 。
2.
In this paper, symmetric solution with exactly one local maximum point is constructed for a singularly perturbed Neumann problem.
讨论了在对称区域上 ,奇异扰动Neumann问题只有一个局部最大值点的对称解 。
2) singular perturbation
奇异扰动
1.
To solve the stability analysis problem aris-ing from the integral term,we employ the singular perturbation theory to analyze the stability of the resulting closed-loop system.
闭环系统的稳定性证明采用了奇异扰动理论,以解决积分项的存在带来的稳定性分析问题。
2.
Based on the singular perturbation theory, the flight control system of MRV was divided into two loops, and the TLC controllers were designed for both loops.
基于奇异扰动原理,将MRV飞行控制系统分为内外两个回路,并且为两个回路都设计了轨迹线性化控制器。
3) singular perturbation theory
奇异扰动理论
1.
Further simplification of the control design process could be realized by dividing the rotorcraft dynamics into translational dynamics and attitude dynamics by using singular perturbation theory.
针对复杂的超小型旋翼机系统,利用牛顿-欧拉方法建立了其系统动力学模型,包括了希勒翼的动力学;为了简化控制器设计,利用奇异扰动理论,把复杂的动力学模型降阶为两个子系统,即平移动力学和姿态动力学;采用非线性逆动力学设计了输出跟踪控制器。
4) geometric singular perturbation theory
几何奇异扰动理论
1.
For vector disease model with distributed delay,when the distributed delay kernel is the general Gamma distribution delay kernel,the existence of travelling wave solutions is obtained by using the linear chain trick and geometric singular perturbation theory.
对于带有分布时滞带菌者的疾病模型,当分布时滞核是—般的г分布时滞核时,通过线性链技巧和几何奇异扰动理论,本文证明带菌者的疾病模型行波解存在性。
2.
Under the condition that the distributed delay kernel is the strong kernel,by the linear chain trick and geometric singular perturbation theory,the existence of travelling wave solutions for the two-species competition-diffusion model with nonlocal delays is obtained.
在分布时滞核是强核的条件下,通过线性链技巧(linear chain trick)和几何奇异扰动理论,获得带有非局部时滞2个物种竞争扩散模型行波解的存在性。
5) normal hyperbolic geometric singular perturbation theory
正规双曲奇异扰动理论
6) singular perturbation method
奇异微扰法
补充资料:持续作用扰动下的稳定性
持续作用扰动下的稳定性
stability in the presence of persistently acting perturbations
持续作用扰动下的稳定性仁咖幽勺协触脚。曰盆兄of哪滋众团ya曲嗯碑由州画d.侣;yc功后”.即c几np班noc”-,。110朋益e拍即IO四,x BO3M脚日e朋,xj 初值问题 交=f(x,r),x(t。)二x。,x任R”(*)之解x。(t)(t)t。)的如下性质:对每一个。>O都有一个占>O使得对每一个适合不等式!y。一x。}<占的夕.,,以及满足以下条件的每一个映射g(x,:): a)在集合 E:={(x,t):t)t。,{x一x。(t)i<。}上g和g,都连续; b)s印(:,,)。::}夕(x,t)一f(x,t)I<吞,初值问题 乡=g(y,t),夕(t。)=夕。,夕任R”的解y。(t)对一切t)屯,有定义且满足不等式 suP}y。(t)一x。(t)}<£. r)t。 Bohi定理(B心h】t玩”~)(【11).设初值问题(,)有解x(t),t)t。,满足以下条件: 幻f和fx对某个。。在瓦。上连续; 刀)s叩。,:。4}人(x(t),t)}}<+的: 下)映射f在点(x(t),‘),t)t。,处对x可微,这个可微性对t)t。是一致的,即 s叩兴}厂(二(‘)+,,,)一f(、(。),:)+ ,》万。}y} 一人(x(t),亡)yl~0当y一,O时.这时,为使初值问题的解在持续作用的扰动下为稳定,必要与充分条件是:方程组又=厂(x,t)沿解x(t)的变分方程(粗血tiona】叹业tio璐)组的上奇异指数(见奇异指数(s泊g止汀exponents))小于零. 若f(x,t)不含t(即自治系统),而解x(t)为周期的或常值的;或者f(x,t)对t有周期而解x(0也有相同的(或可公度的)周期或者常值,则:l)Bohi定理中所陈述的一致可微性条件是多余的(它可从定理的其他条件导出);2)方程组交=f(x,t)沿解x(t)的变分方程组的上奇异指数可以有效地算出来.【补注】持续作用扰动下的稳定性也称为持续扰动下的稳定性(stab正ty Under pelsis招ni perturhatio幻)或全稳定性(total stabiljty).
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