MATH 721, Nonliear Dynamics and Chaos I, Fall 2016

Lectures: Tu 4:00pm - 5:15pm in AB 206 (map); Wed 2:30-3:45pm in WRJ 2020 (map) 29 Aug - 13 Dec, 2016
Office Hours: 220 DMSC. Mondays 1-2pm, Wednesdays 4-5pm, and Thursdays 1-2pm.
Syllabus: Click here to download PDF. Course Catalog Description.

Textbook: Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering 2nd Ed. Author website:

Software Resources

UNR Software: Matlab and Mathematica via DataWorks Remote Services at UNR. Also see the discounts available through the bookstore, software for personal computers, and software available in various computer labs on campus.

R: Install R, then RStudio. Also, see my R page.
Google's Style Guide for R scripts:
I intend to revise my Intro to R (PDF) soon! See also R for Matlab Users, and David Hiebeler's R / Matlab Reference (PDF).

Maxima:A free alternative to Maple for symbolic computations. Download Maxima or the slightly more user friendly version (preferred) wxMaxima.
Maxima Resources: Instant Maxima (PDF) by Steve Ellner. Also, see Richard H. Rand's Introduction to Maxima, or see the Maxima website.

LaTeX Editor: Use TeXStudio if you don't have a preferred editor. This runs on all main operating systems. .
Getting Started with LaTeX: You might find my LaTeX Resources page useful.
Writing Equations in LaTeX: The AMS Short Math Guide for LaTeX (PDF) is excellent!
Homework Template: Want to turn in homework that looks like this PDF? Download this zip file and open the TeX document in TeXStudio.

Tentative Schedule

Week Tuesday Wednesday Homework & Notes
1: 8/30 Syllabus, Schedule, Introduction Basic Definitions (Ch 1)
1D Dynamics (2.1-2.4)
Read Chapter 1 on your own, practice with Piazza. See Lecture 1 video by Strogatz.
Change to new schedule next week!
2: 9/6 1D Dynamics (Ch 2)
1D Bifurcations (Ch 3, 4)
3: 9/13 1D Dynamics & Bifurcations
(Ch 3,4)
Dynamics in 2 Dimensions
(Ch 5)
Homework #1 (Due Tuesday, 9/20): [PDF] [TEX]
Reading for next week: Ch. 5, 6.0-6.3
4: 9/20 Dynamics in 2 Dimensions
(Ch 5-6)
Phase-Plane Analysis Homework #2 (Due Wednesday, 9/28): [PDF] [TEX]
Rpplane-beta: Run app.R in Rstudio.
R code: First see solve-odes.R, then RM-example.R.
Reading for next week: Hethcote (2000) through all of section 2, and textbook Ch. 5-7
5: 9/27 Dynamics in 2 Dimensions
(Ch 6-7)
Limit Cycles (Ch 7) Homework #3 (Due Wednesday, 10/5): [PDF] [TEX]
6: 10/4 Dynamics in Higher Dimensions
(Ch 6-8)
Reading for this week: Tien & Earn (2010) doi:10.1007/s11538-010-9507-6
7: 10/11 Review for exam Exam 1 (Take home; due 10/18) Nondimensionalization Example: [PDF] [TeX]
Linear Stability Analysis in wxMaxima: stability2D.wxmx, stability3D.wxmx
8: 10/18 Exam 1 DUE
Bifurcations revisited
(Ch 7-8)
Center Manifolds and Normal Forms
9: 10/24 Computational Bifurcation Analysis Computational Bifurcation Analysis Download and install Matcont for Matlab.
10: 11/1 Stability and Bifurcation Analysis Chaos (Part III; Ch. 9) REMINDER: Class on Tuesday now in DMSC 106!
11: 11/8 Stability and Bifurcation Analysis Discrete Maps RMeqstability.wxmx
cobweb0.R, cobweb.R, cobweb-tent.R
12: 11/15
13: 11/22
14: 11/29
15: 12/6 vdp-euler.R, lorenz.R
stochastic-simulations.R, ssa.R
16: 12/13 fitting-ode-to-data.R,