Department of Earth and Atmospheric Sciences

The course will cover the basic topics of applied nonlinear dynamics and time series analyses, with the tentative topics as follows:

Part 1: Nonlinear dynamics

• Flows, maps, fixed points, invariant sets
• Planar ODEs and Taylor's theorem 
• Lyapunov functions, attractors, and stability analyses
• Poincare-Bendixson theorem and return maps
• Bifurcations and classifications 
• Center manifold theorems 

Part 2. Nonlinear time series

• Phase-space reconstruction
• Chaotic attractor and invariants
• Spectral analyses and noise filtering