微分方程定性方法和数值模拟

Chapter 1 Phase Port.raits of Linear Systems1.1 Standard Forms of Linear Systems1.2 Classification of Singular Points for Linear Systems1.3 Phase Portraits and Their Simulation for Some Linear Syst.emsChapter 2 Properties of Singular Points of Nonlinear Systems with Nonzero Eigenvalues2.1 The Linear Approximate Principle2.2 The Detection Method for Cent.er or Focus of Quadratic Systems2.3 The Detection Method for Center or Focus of General SystemsChapter 3 Properties of Singular Points of Nonlinear Systems with Zero Eigenvalues3.1 Property of Singular Point （0，0） of System （3.6） with Only a Zero Eigenvalue3.2 Property of Singular Point （0，0） of System （3.6） with Two Zero EigenvaluesChapter 4 High Degree Singular Points4.1 Case of G（O） 4.2 Case of G（O） Chapter 5 Limit Cycles and 1Fheir Bifurcation5.1 Some Definitions and Examples on Limit Cycles and Their Bifurcation5.2 Limit Cycles and Their Bifurcation for Perturbed Hamiltonian Systems5.3 Non-Existence of Closed OrbitsChapter 6 Infinite Singular Points and Indice6.1 Infinite Singular Points6.2 Indice of Curves and Singular PointsChapter 7 An Application of Phase Portraits7.1 Traveling Wave System and Its Bifurcation Phase Portraits7.2The Peakon Wave Solutions7.3 The Singular Wave Solutions7.4 The Smooth Solitary Wave SolutionsReferences

《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。