Applied Math 3010, Fall 2016

Nonlinear Dynamical Systems and Chaos

- We will do the Standard Map Lab on Wed 11/29 in Claire 111. Be there!

Class: | MWF 12 | FLMG 103 |

Instructor: | J. Meiss | ECOT 236 |

Office Hours: | M 2:00-3:30, W 1:30-3:00 | Other times--by appointment |

Text | Strogatz, S. | Nonlinear Dynamics and Chaos (2nd Edition, WestView Press) |

Chaos is a relatively new area of applied mathematics that has influenced everything from spacecraft trajectories, the design of lasers, ultrafast spectroscopy, the design of micro-mixers, and stock market analysis to even psychology, drama, and literature. Our study will begin with simplest of systemsâ€”one dimensional dynamics and progress to systems with more degrees of freedom (We will move nonlinearly through the text!). Our study includes differential equations and maps, bifurcations and catastrophes, and the qualitative analysis of dynamical systems. The emphasis will be on dynamics that model real world phenomena.

- Course syllabus (pdf file)
- The current schedule and HW assigments
- Final Projects (Final Due Dec 9)

A (somewhat out of date!) list of software for dynamics—much of it free—is at <http:// amath.colorado.edu/faculty/jdm/faq-[5].html>. I will use a Macintosh (or iPad) for classroom demonstrations, and extensively use the software Maple and Matlab.

- Macintosh Programs
- Maple examples
- Matlab files
- Vector Fields: vectorField.m (uses quiver for plots),
- Simple Numerical Methods: Euler.m (1st order Euler), ImprovedEuler.m (2nd order Euler), f.m (a typical ode),
- to make a cobweb diagram: cobweb.m of theMap.m
- Feigenbaum scaling: Logistic Map, Supertable Orbit Finder, Feigenbaum Delta.
- To iterate the Henon Map: henon.m, iterate.m,
- To compute the box dimension of the Henon attractor: boxdim.m
- To find the Lyapunov exponent: lyapunov.m and DHenon.m for the Jacobian
- To find the basin of attraction: basinHenon.m
- To draw phase portraits of ODEs in 2D: pplane (note: this does not work with recent matlab versions, but here is a version that I've fixed to some extent).

- Mathematica Examples
- DynPac Dynamical Systems Package

- Java Applets
- Pplane and Dfield (Rice Univ.)
- Fractal Grower by Joel Castellanos
- Chaos for Java (ANU, Canberra)
- Math Visualization Toolkit (CU APPM)
- Physics Simulations (by Erik Neumann) see also the html5 versions

- Python Code