APPM 3010, Intro/Nonlinear Systems: Chaos, Fall 2017
News
- https://www.colorado.edu/amath/sites/default/files/attached-files/hw1_2…; Posted Due Friday Sept. 15th.
- https://www.colorado.edu/amath/sites/default/files/attached-files/hw2_2…; Posted Due Wednesday Oct. 4th.
- https://www.colorado.edu/amath/sites/default/files/attached-files/hw3_2…; Posted Due Monday Oct. 23th.
- https://www.colorado.edu/amath/sites/default/files/attached-files/hw4_2…; Posted Due Wednesday Nov. 15th.
- https://www.colorado.edu/amath/sites/default/files/attached-files/hw5_2…; Posted Due Monday Dec. 18th.
Course Information
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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 systems—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.
- https://www.colorado.edu/amath/sites/default/files/attached-files/sylla… syllabus (pdf file)
- https://www.colorado.edu/amath/sites/default/files/attached-files/sched… current schedule and HW assigments
- https://www.colorado.edu/amath/sites/default/files/attached-files/proje… Projects (Topic Choice by Oct 9. Written project due Dec 15)
Computers
A (somewhat out of date!)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">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.
Programs & examples
Macintosh Programs
- http://amath.colorado.edu/faculty/jdm/1DMaps.html">One Dimensional Map Program
- http://amath.colorado.edu/faculty/jdm/stdmap.html">Standard Map Program
- http://amath.colorado.edu/faculty/jdm/ifs.html">Iterated Function Systems Program
- http://physics.wooster.edu/Software/">College of Wooster Software, See http://physics.wooster.edu/Lindner/software/ThreeBody/">Three-Body Problem as well as others.
- http://amath.colorado.edu/faculty/juanga/3DAttractors.html">Juan Restrepo's 3D Attractors
Maple examples
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/PhasePortrait… Phase Portraits
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/NumericalMeth… Methods for ODEs
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/Zeeman Catastrophe Machine.mw">Zeeman's Catastrophe Machine (http://amath.colorado.edu/faculty/jdm/3010/examples/maple/Zeeman.pdf">P… file)
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/logisticani.m… Diagram for Logistic Map
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/LogisticPerio… 3 orbits of the Logistic Map
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/Lorenz.mw">Lo… system
- http://amath.colorado.edu/faculty/jdm/3010/examples/maple/Rossler.mw">R… system
Matlab files
- Vector Fields: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/vectorField…; (uses quiver for plots),
- Simple Numerical Methods: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/Euler.m">Eul…; (1st order Euler), http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/ImprovedEule…; (2nd order Euler), http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/f.m">f.m; (a typical ode),
- to make a cobweb diagram: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/cobweb.m">co…; of http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/theMap.m">th… scaling: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/Logistic.m">… Map,http://amath.colorado.edu/faculty/jdm/3010/examples/Superstable.m">; Superstable Orbit Finder, http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/feigenbaum.m… Delta.
- To iterate the Henon Map: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/henon.m">hen… href="http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/iterate.m">; http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/iterate.m">i… href="http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/iterate.m">,… compute the box dimension of the Henon attractor: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/boxdim.m">bo… find the Lyapunov exponent: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/lyapunov.m">…; and http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/DHenon.m">DH…; for the Jacobian
- To find the basin of attraction: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/basinHenon.m…;
- To draw phase portraits of ODEs in 2D: http://amath.colorado.edu/faculty/jdm/3010/examples/matlab/pplane8.m&qu…; target="_blank">pplane (this is a version modified to mostly work with Matlab 2016)
Mathematica Examples
Java Programs
- http://math.rice.edu/~dfield/dfpp.html">Pplane and Dfield (Rice Univ.)
- http://www.clickrepair.net/chaos/software.html">Chaos for Java (ANU, Canberra)
- http://amath.colorado.edu/java/">Math Visualization Toolkit (CU APPM)
Policies
- https://www.colorado.edu/amath/academics/student-resources/policies/dis… Services
- https://www.colorado.edu/amath/academics/student-resources/policies/rel… Observances
- https://www.colorado.edu/amath/academics/student-resources/policies/cla… Behavior
- https://www.colorado.edu/amath/academics/student-resources/policies/dis… and Harassment
- https://www.colorado.edu/amath/academics/student-resources/policies/aca… Honesty and Honor Code
- http://www.colorado.edu/policies/final-examination-policy">Final Examination Policy