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Introduction to Dynamical Systems - Lecture 1
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- 1 Start
- 2 Example: Discrete-time
- 3 ODE:
- 4 Equilibrium points
- 5 Example
- 6 Solution of linear ODEs
- 7 Eigenvalues and eigenvectors
- 8 Calculation of eigenvalues
- 9 Complex eigenvalues
- 10 3D systems
- 11 On to nonlinear systems
- 12 Attractors in nonlinear systems
- 13 Limit cycle
- 14 The Lorenz system
- 15 Chaos
- 16 Orbit on a torus
- 17 Q&A
- 18 The Poincare section
- 19 The Poincare map
- 20 One-dimensional maps
- 21 Graphical iteration
- 22 Stability of fixed points
- 23 Bifurcation diagram
- 24 Saddle-node bifurcation
- 25 Period doubling bifurcation
