Nonlinear Dynamics & Stability
A 16-module path through nonlinear dynamics & stability, in study order from foundations to the frontier.
Modules
- Autonomous Systems and Phase Space
- Fixed Points and Equilibria
- Linearization and the Jacobian
- Classification of Planar Fixed Points
- Hartman-Grobman and Hyperbolicity
- Stability Concepts and Definitions
- Lyapunov Functions and Stability
- Conservative Systems and the Pendulum
- Limit Cycles and Closed Orbits
- The Poincare-Bendixson Theorem
- Bifurcations in One Dimension
- Saddle-Node, Transcritical, and Pitchfork Bifurcations
- Hopf Bifurcation
- Chaos and Sensitive Dependence
- The Lorenz System
- Discrete Maps: The Logistic Map and Period-Doubling