Contents Chapter 1: Introduction 1.1 Qualitative analysis 1.2 Definitions and notations 1.3 Equilibrium points and linearization Chapter 2: Linear Systems 2.1 Linear systems in R2 2.2 Exponential of matrices 2.3 Distinct eigenvalues 2.4 Multiple eigenvalues 2.5 Asymptotic behaviour 2.6 Contractions and expansions Chapter 3: Nonlinear Systems 3.1 Nonlinear sinks and sources 3.2 Fundamental theory 3.3 The flow defined by ODEs 3.4 The Hartman-Grobman theorem 3.5 Stability of equilibria 3.6 Hamiltonian systems 3.7 Limit sets and long-term behaviour Chapter 4: Periodic Solutions and Bifurcations of Vector Fields 4.1 Limit cycles and separatrix cycles 4.2 Dulac's criteria 4.3 Poincaré-Bendixson theorem 4.4 Lienard systems 4.5 Structural stability and bifurcation 4.6 Hopf bifurcations Appendix A: Maple Worksheet A.1 Maple worksheet for chapter 2 A.2 Maple worksheet for chapter 3 A.3 Maple worksheet for chapter 4 Appendix B: ODE Phase Portraits Plotter Next: Introduction Up: AM451 Home Page Previous: AM451 Home Page
