在這篇論文中，我們分析未決定投票傾向選民的心理。提出兩個模型，分別描述沉默的螺旋現象和擁有較高支持率候選人的選民也會變成沉默的情形。根據模型一和模型二，得到微分方程組，討論與證明非線性系統中的穩定性。提出一個選舉預測的方法。預測兩個候選人的支持度。用我們提出的方法預測了美國和台灣二十次的選舉。

In this paper, we analyze the psychology of undecided voters. We
propose two models. Model 1 describes the phenomena of Spiral of
Silence Theory. Model 2 describes the phenomena that a supporter
of opinions with a high approval rate to become silent. We derive
a system of nonlinear differential equations for Model 1 and Model
2. We also discuss the stability of the equilibrium points of the
nonlinear systems. We propose an election prediction method based
on the models. We predict the percentages of votes obtained by the
candidates in twenty real election cases.

Contents
Contents 1
List of Tables 3
List of Figures 4
1 Introduction 5
2 Model 9
3 Analysis 13
3.1 model 1 . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 An Election Prediction Method 21
5 Numerical Results 25
5.1 Numerical Results . . . . . . . . . . . . . . . . . . . 25
5.2 Election Prediction Method Results . . . . . . . . . . 29
6 Future Work and Conclusion 32
6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . 32
6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 33
Bibliography 34
Appendix 37
A Prove Lemma 3.1.1 and Proposition 3.1.2 37
B Prove Proposition 3.2.1 41
C Prove Proposition 4.0.1 43

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