Math 5470/6440   Chaos and Nonlinear Systems
T Th     9:10 am - 10:30 am     LS 101

  Text:  Nonlinear Dynamics and Chaos 
           by  Steven Strogatz

  Instructor:   Prof. Elena Cherkaev
   Office: LCB 206   ph: 581-7315  
   email:   elena@math.utah.edu
  (please write  5470  in the subject line)
   Office hours: T 10:30-11:30 am and by appointment

  Class webpage:  http://www.math.utah.edu/~elena/M5470/5470.html

  Steven Strogatz on synchronization
Explore fractals at http://users.math.yale.edu/public_html/People/frame/Fractals/

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  Assigned Homework:  
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Bold-faced problems = "must solve", the rest is recommended
Jan 11:  
Ex 2.2  #  34,  6,  7,   8,  10,  12;   Ex 2.3    2,  4,  5,  6
Jan 16:   Ex 2.4  #  1, 2, 3, 4, 5
 
                      Ex 2.6  #  1
Jan 18:   Ex 3.1  #  1, 3;    Ex. 3.2  #  2, 4
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Course description
Chaos is everywhere around us from fluid flow and the weather forecast to the stock exchange and striking geometric images. The theory of nonlinear dynamical systems uses bifurcations, attractors and fractals to describe the chaotic behavior of real world things. The course gives an introduction to chaotic motions, strange attractors, fractal geometry. The emphasis of the course is on applications:


  • Mechanical vibrations
  • Chemical oscillators
  • Superconducting circuits
  • Insects outbreaks
  • Genetic control systems
  • Chaotic waterwheels 
  • Chaotic communications


The course is addressed to senior undergraduate and graduate students in mathematics, science and engineering. Prerequisites: Calculus and Differential Equations.

Tentative Course Schedule:

 Part I: Jan 8 - Jan 25  -- Flows on the line. Bifurcations.  Flows on the circle
.
 Part II: Jan 30 - Mar 6  -- Linear systems: Phase plane. Limit Cycles. Bifurcations.
 Part III: Mar 6 - Apr 24
  -- Lorentz equations. 1D Iterated maps. Fractals. Strange attractors.

Exams:
  There will be two midterms and an optional project and/or final exam. Tentative dates for the midterms:  Feb 22;   Apr 12.
Final test:  Friday, April 27, 2018,  8:00 – 10:00 am

Grading:  The grade will be calculated as an average of the midterms and the project and/or final.


Holidays:   Martin Luther King Jr. Day:  Monday, January 15;    Presidents' Day: Monday, February 19
Spring break:   March 18-25


Computer lab set up:  Maple example (slope field)
Maple: Lorenz attractor  
For Matlab, download  dfield8 and pplane8 from John C. Polking's website: http://math.rice.edu/~dfield/index.html#8.0
Java simulator:   http://chaos.wlu.edu/106/programs/lorenzdes.html


ADA statement:  The American with Disabilities Act requires that reasonable accommodations be provided for students with physical, systemic, learning, and other disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.