V2EX limit cycle

Limit Cycle

Definition / 释义

Limit cycle(极限环):在非线性动力系统中,系统在相空间里形成的一个孤立的闭合轨道;附近轨道会随着时间演化趋近它(稳定极限环)或远离它(不稳定极限环)。常用来描述自激振荡的长期稳定周期行为。

Pronunciation / 发音

/lmt sakl/

Examples / 例句

A limit cycle can produce a steady rhythm in a system.
极限环可以在系统中产生稳定的节律。

In the phase plane, trajectories spiral toward a stable limit cycle, showing sustained oscillations even without external forcing.
在相平面中,轨线会向稳定极限环螺旋靠近,表明即使没有外部驱动也会出现持续振荡。

Etymology / 词源

limit 源自拉丁语 *limes/limit-*,有“边界、界限”之意;cycle 源自希腊语 kyklos,意为“圆、循环”。合在一起,“limit cycle”字面上可理解为“作为(行为)界限的循环”:它描述一种“最终会被系统吸引到(或排斥开)的周期轨道”,像是系统长期演化的“边界型周期运动”。

Related Words / 相关词

Notable Works / 作品举例

  • Nonlinear Dynamics and Chaos Steven H. Strogatz
  • Differential Equations, Dynamical Systems, and an Introduction to Chaos Morris W. Hirsch, Stephen Smale, Robert L. Devaney
  • Nonlinear Oscillations A. A. Andronov, A. A. Vitt, S. E. Khaikin
  • Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers D. W. Jordan, P. Smith
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