V2EX phase plane

Phase Plane

Definition / 定义

相平面:在动力系统与微分方程中,用两个状态变量作为坐标的平面,用来描绘系统状态随时间演化的轨迹(相轨线)、平衡点与其稳定性等。(常见于二维自治系统;更高维时称 phase space “相空间”。)

Pronunciation / 发音

/fez plen/

Examples / 例句

The phase plane shows how the system moves between states.
相平面展示了系统如何在不同状态之间演化。

By sketching trajectories in the phase plane, we can classify equilibria and predict whether solutions spiral, approach a limit cycle, or diverge.
通过在相平面中描绘轨迹,我们可以分类平衡点,并预测解是螺旋收敛、趋向极限环,还是发散。

Etymology / 词源

phase 源自希腊语 phasis(“显现、出现”),在科学语境中引申为“状态/相位”;plane 源自拉丁语 planus(“平的”)。组合成 phase plane,字面义为“用一个平面来表示系统的状态(相)变化”,用于二维系统的几何分析与可视化。

Related Words / 相关词

Literary Works / 文学与名著用例

  • Steven H. Strogatz, Nonlinear Dynamics and Chaos(常用相平面图分析非线性系统与极限环)
  • Lawrence Perko, Differential Equations and Dynamical Systems(相平面方法与定性理论的经典教材)
  • John Guckenheimer & Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields(大量使用相平面与相图分析分岔与振荡)
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