Math 5470/6440   Nonlinear Dynamics and Chaos
T H     10:45 am - 12:05 pm     WEB L112

Text:  Nonlinear Dynamics and Chaos 
           by  Steven Strogatz

Instructor:   Prof. Elena Cherkaev
Office: LCB 206   ph: 581-7315   email: elena@math.utah.edu
Office hours: M 2-3pm and by appointment

Syllabus     

Feb 10 : Midterm 1 - Chapters 2, 3, 4.   Sample test (last year exam)
               Solutions to selected hw problems:  Ch2, Ch3-4

March 26 : Midterm 2 - Chapters 5, 6, 7, 8 (1-2).   Sample test (last year exam)
               Solutions to selected hw problems:  Ch6,  Ch7-8
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Assigned Homework Problems:  
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Jan 10:    Ex 2.2  #  3,  4,  6,  7,   8,  12.      Ex 2.3    2,  3,  4 .    Ex 2.4  #  2,  4,  7,  8,  9 
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Jan 15:    Ex 2.7  #  1,  2,  4,  6,  7.    Ex 3.1  #   1,  3
Jan 17:   Ex 3.2  #   2,  4,  6.    Ex 3.3  #   1, 2.    Ex 3.4  #   3,  8,  14,  15,  16
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Jan 22:    Ex  3.6  #    2,  3,   6.  
Jan 24:    Ex  3.7  #    3,  4,  5,  6.   Ex 4.1  #    2,  3,  4,  8. 
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Jan 29:   Ex 4.2  # 1,  2,  3.   Ex  4.3   #  1,  2,   3,  5,  7 ;  Ex  4.5  #  1,  3;  
                                       Steven Strogatz on synchronization
Jan 31:    Ex  5.1  #  9,  10,  11
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Feb 12:    Ex  5.2  #   2,  7,  9, 13;  Ex  5.3  #   2-6
Feb 14:     Ex  6.1   # 1,  4,  6;      Ex  6.2  # 2;     Ex  6.3   # 2,  3
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Feb 19:      Ex  6.3   #   14, 15
Feb 21:      Ex  6.4   #   1,  2,  3;    Ex  6.5   #   1, 8,  9
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Feb 26:      Ex  6.5   #   2,  3,  4;    Ex  6.8    #   6,  7,  8 , 11, 13
Feb 28:     
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Mar 5:      Ex  7.1    #  1-5, 7, 8;    Ex  7.2  #  1-3,  6,  9
Mar 7:      Ex  7.3   #  6,  7;    Ex   7.5   #  3, 4
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        ----       Spring break       March 10-17             -----  
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Mar 19:    Ex  8.1  #  1-4,  5,   11 ;   Ex  8.2   # 1,  2,  8
Mar 21:     Ex  8.3  # 1;   Ex  8.4   # 1,  2;  
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Mar 26:   
Mar 28:     Ex  8.6  # 1, 3  ;  Ex  8.7   # 1,  3,  9
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Apr 2:    Ex  9.1  # 4;   9.2  # 3,  6 
Apr 4:     Ex  9.3  # 1,   2-7,   9-10;  Ex  9.4  #  2.  Play with lorenz attractor in maple
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Apr 9:   
Apr 11:
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Apr 16: 
Apr 18:    
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Apr 23: 
Apr 25:    
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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 31  -- Flows on the line: Jan 8-15.  Bifurcations: Jan 17-24.  Flows on the circle: Jan 29-Jan 31.
 Part II: Feb 5 - Mar 7  -- Linear systems: Feb 5-7. Phase plane: Feb 12-14. Limit Cycles: Feb 19-26. Bifurcations: Feb 28-Mar 7.
 Part III: Mar 19 - Apr 23  -- Lorentz equations: Mar 19-26. 1D Iterated maps:  Mar 28-Apr 4. Fractals:  Apr  9-16. Strange attractors: Apr 18-23.

Exams:  There will be three midterms and an optional project and/or final exam. Tentative dates for the midterms:  Feb 7;  Mar 21;  Apr 23.
Final test:  Tuesday, April 30,  10:30 am -- 12:30 pm  

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 21;    Presidents' Day: Monday, February 18.
Spring break:   March 10-17.


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, sensory, cognitive, systemic, and learning, and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.