這篇文章我們想要討論如何去建構一個Psi級數解滿足二次多項式微分方程。
我們想要了解在靠近歧異點的時候解的行為。
那我們有一個若且為若的條件保證：若解在有線時間內趨近無窮大若且為若解的係數皆為實數。
所以我們在這邊探討一個擬態物理中的常微分方程的二微與三微情形。

In this paper, we discuss how to build a local solution for a system of ordinary differentiable equations of quadratic forms by constructing a psi-series. We want to understand how the solution behaves around the singularities. There
are a necessary and sufficient condition: Real leading coefficients ensure the occurrence of blow up in finite time, and real time singularity implies that the
leading coefficients of one asymptotic series are real.
The Psi-series of quadratic systems on the plane has been studied. The relationship between the behavior and integrability of the system is also illustrated.

[1] Alain Goriely,Craig Hyde, Necessary and Sufficient Conditions for Finite Time Singularities in Ordinary Differential Equations, JDE 161, 422-448 (2000).
[2] Arnau Mir , Amadeu Delshams ,Psi-Series of Quadratic Systems on the Plane (1995)
[3] Hong-Yan Shih, Wen-Min Huang, Sze-Bi Hsu, and Hsiu-Hau Lin, Hierarchy of relevant couplings in perturbative renormalization group transformations,PHYSICAL REVIEW B 81, 121107 R (2010)