V2EX nullcline

Nullcline

释义 Definition

零流线 / 零斜线(nullcline):在二维自治微分方程(相平面系统)中,使某一个分量的导数为零的曲线。
例如对系统 \(x' = f(x,y),\; y' = g(x,y)\),满足 \(f(x,y)=0\) 的曲线叫 x-nullcline,满足 \(g(x,y)=0\) 的曲线叫 y-nullcline。两条 nullcline 的交点常对应系统的平衡点/固定点。(该词在更高维也可推广为“零导数集合”。)

发音 Pronunciation (IPA)

/nl.klan/

例句 Examples

The nullclines intersect at an equilibrium point.
零流线在一个平衡点处相交。

By plotting the x-nullcline and y-nullcline, we can sketch the phase portrait and predict how trajectories move near the fixed points.
通过绘制 x-零流线和 y-零流线,我们可以勾画相图,并预测轨线在固定点附近的运动方式。

词源 Etymology

nullcline 由 **null-**(“零、无”,源自拉丁语 nullus)+ -cline(“倾斜/坡度/线”,与“斜率、倾向”相关,源自希腊语词根 klinein “倾斜”)构成,字面意思接近“导数为零的那条线”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Steven H. Strogatz, Nonlinear Dynamics and Chaos(常用 nullclines 分析二维系统与极限环)
  • Lawrence Perko, Differential Equations and Dynamical Systems(相平面分析中系统讲解 nullclines)
  • James D. Murray, Mathematical Biology(用 nullclines 研究捕食-被捕食等模型的平衡与稳定性)
  • Morris W. Hirsch, Stephen Smale, Robert L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos(相关章节常出现 nullcline 概念)
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