在本文中，我們探討范得坡方程式x''+μx'(x^2-1)+x=0在相平面上的一
條特殊軌線 記為y_(∞)(x;μ)，它是范得坡方程式在相平面上的極限
環在某區域中的漸近解。我 們證明在相平面的上半平面中，當μ →
+∞，對於[-1,0]區間中的每個 x，極限環與 y_(∞)(x;μ)的y座標差至
多為O(μ^(-1/3))；更進一步，應用這個結果，可以證明 當μ →
+∞，相平面上每一條從 y 軸出發且在極限環外部的范得坡方程式的軌線
，自 第一次與 x=1 相交於第四象限之後，其與極限環的誤差至多為O(μ
^(-1/3))。

This article is concerned with the special trajectory y_(∞)(x;
μ) which is the leading term of the asymptotic solution
of Van der Pol equation x''+μx'(x^2-1)+x=0 in the phase
plane for some region. We show that in the phase plane,
the difference of this asymptotic solution and the limit
cycle, y_(p)(x), of Van der Pol equation is not greater than
O(μ^(-1/3)) as μ → +∞ for all -1 ＜ x ＜ 0, and use this
result to show that every trajectory of Van der Pol equation
starting from y-axis with initial value bigger than that
of the limit cycle gets close to the limit cycle by O(μ
^(-1/3)) from its first time on for intersecting x=1 in the
fourth quadrant as μ → +∞.
This article is concerned with the special trajectory y_(∞)(x;