刘正荣编著的《微分方程定性方法和数值模拟（英文版）》是本科生的《常微分方程》教材的后续教材，是为高年级本科生或研究生的选修课程编写的英语教材。本书包含线性系统的相图，非线性系统的线性近似，具有零特征值奇点的性质，高阶奇点，极限环和它们的分支，无穷远奇点及奇点指数，关于相图应用的例子等内容。

刘正荣编著的《微分方程定性方法和数值模拟（英文版）》包含线性系统的相图，非线性系统的线性近似，具有零特征值奇点的性质，高阶奇点，极限环和它们的分支，无穷远奇点及奇点指数，关于相图应用的例子等内容。《微分方程定性方法和数值模拟（英文版）》可作为高等院校数学类、自动化控制、信息处理等专业的本科生和研究生的选修课教材，也可作为对微分方程及数值模拟感兴趣的朋友的自学读本。

Chapter 1 Phase Port.raits of Linear Systems

1.1 Standard Forms of Linear Systems

1.2 Classification of Singular Points for Linear Systems

1.3 Phase Portraits and Their Simulation for Some Linear Syst.ems

Chapter 2 Properties of Singular Points of Nonlinear Systems with Nonzero Eigenvalues

2.1 The Linear Approximate Principle

2.2 The Detection Method for Cent.er or Focus of Quadratic Systems

2.3 The Detection Method for Center or Focus of General Systems

Chapter 3 Properties of Singular Points of Nonlinear Systems with Zero Eigenvalues

3.1 Property of Singular Point （0,0） of System （3.6） with Only a Zero Eigenvalue

3.2 Property of Singular Point （0,0） of System （3.6） with Two Zero Eigenvalues

Chapter 4 High Degree Singular Points

4.1 Case of G（O）

4.2 Case of G（O）

Chapter 5 Limit Cycles and 1Fheir Bifurcation

5.1 Some Definitions and Examples on Limit Cycles and Their Bifurcation

5.2 Limit Cycles and Their Bifurcation for Perturbed Hamiltonian Systems

5.3 Non-Existence of Closed Orbits

Chapter 6 Infinite Singular Points and Indice

6.1 Infinite Singular Points

6.2 Indice of Curves and Singular Points

Chapter 7 An Application of Phase Portraits

7.1 Traveling Wave System and Its Bifurcation Phase Portraits

7.2The Peakon Wave Solutions

7.3 The Singular Wave Solutions

7.4 The Smooth Solitary Wave Solutions

References