sfi-nonlinear-dynamics

This is some toy code lying around I wrote for the Nonlinear Dynamics: Mathematical and Computational Approaches SFI course by instructor Prof. Liz Bradley.

The course was broken down into:

1. Introduction and Maps I
   1. Introduction to nonlinear dynamics
   2. Maps and difference equations
   3. Transients and attractors
   4. Parameters and bifurcations
   5. Field trip: Boulder Creek
2. Maps II
   1. Return maps
   2. Constructing the bifurcation diagram
   3. Exploring the bifurcation diagram
   4. Feigenbaum and universality
   5. Field trip: The standard map (with Jim Meiss)
3. Flows I
   1. What is a flow?
   2. State variables and state space
   3. Introduction to ODEs
   4. Nonlinearity and nonintegrability
   5. Field trip: ODEs and the human insulin system (with Sriram Sankaranarayanan)
4. Flows II
   1. Fixed points and stability
   2. Saddle points and eigenvectors
   3. Stable and unstable manifolds
   4. Attractors, strange and otherwise
   5. Field trip: Using stable and unstable manifolds to design spacecraft trajectories (with Jeff Parker)
5. Flows III
   1. ODEs, vector fields and dynamical landscapes
   2. Introduction to ODE solvers
   3. Forward and backward Euler
   4. Solving the SHO ODEs
   5. Field trip: Systems that can't be modeled with ODEs (with Jean Hertzberg)
6. Flows IV
   1. ODE solvers II: Error and adaptation
   2. Production ODE solvers
   3. Numerical dynamics and due dilligence
   4. Shadowing and chaos
   5. Field trip: Solving PDEs (with Christine Hrenya)
7. Flows V
   1. Dynamics and state-space deformation
   2. Lyapunov exponents
   3. Sections and projections
   4. Unstable periodic orbits
   5. Fractals and chaos
   6. Field trip: Diffusion-limited aggregation, fractals and snowflakes (with Dave Feldman)
8. Nonlinear time-series analysis I
   1. Time-series analysis and the observer problem
   2. Delay-coordinate embedding
   3. Topology, diffeomorphisms and reconstruction of dynamics
   4. Estimating embedding parameters
   5. Caveats and extensions
   6. Field trip: Detecting extreme events (with Holger Kantz)
9. Nonlinear time-series analysis II
   1. Computing fractal dimensions
   2. Computing Lyapunov exponents
   3. Noise and filtering
   4. Field trip: Chaotic mixing and marine invertebrate reproduction (with John Crimaldi)