-
-
Introduction to nonlinear dynamics
-
Maps and difference equations
-
Transients and attractors
-
Parameters and bifurcations
-
Field trip: Boulder Creek
-
Maps I: Unit test
-
-
-
Return maps
-
Constructing the bifurcation diagram
-
Exploring the bifurcation diagram
-
Feigenbaum and universality
-
Field trip: The standard map (with Jim Meiss)
-
Maps II: Unit test
-
-
-
What is a flow?
-
State variables and state space
-
Introduction to ordinary differential equations (ODEs)
-
Nonlinearity and nonintegrability
-
Field trip: ODEs and the human insulin system (with Sriram Sankaranarayanan)
-
Flows I: Unit test
-
-
-
Fixed points and stability
-
Saddle points and eigenvectors
-
Stable and unstable manifolds
-
Attractors, strange and otherwise
-
Field trip: Using stable and unstable manifolds to design spacecraft trajectories (with Jeff Parker)
-
Flows II: Unit test
-
-
-
ODEs, vector fields, and dynamical landscapes
-
Introduction to ODE solvers
-
Two simple ODE solvers: forward and backward Euler
-
Solving the simple harmonic oscillator ODEs
-
Field trip: Systems that can't be modeled with ODEs (with Jean Hertzberg)
-
Flows III: Unit test
-
-
-
ODE solvers, round II: Error and adaptation
-
Production ODE solvers
-
Numerical dynamics and due diligence
-
Shadowing and chaos
-
Field trip: Solving partial differential equations (with Christine Hrenya)
-
Flows IV: Unit test
-
-
-
Dynamics and state-space deformation
-
Lyapunov exponents
-
Sections and projections
-
Unstable periodic orbits
-
Fractals and chaos
-
Field trip: Diffusion-limited aggregation, fractals, and snowflakes (with Dave Feldman)
-
Flows V: Unit test
-
-
-
Time-series analysis and the observer problem
-
Delay-coordinate embedding
-
Topology, diffeomorphisms, and reconstruction of dynamics
-
Estimating embedding parameters
-
Caveats and extensions
-
Field trip: Detecting extreme events (with Holger Kantz)
-
Nonlinear time-series analysis I: Unit test
-
-
-
Computing fractal dimensions
-
Computing Lyapunov exponents
-
Noise and filtering
-
Field trip: Chaotic mixing and marine invertebrate reproduction (with John Crimaldi)
-
Nonlinear time-series analysis II: Unit test
-
-
-
Prediction
-
Control of chaos
-
Classical mechanics
-
Music and dance (with a coda on the difference between chaos and complexity)
-
Applications: Unit test
-
Nonlinear Dynamics: Mathematical and Computational Approaches (Fall 2016)
Lead instructor: Liz Bradley