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