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Introduction to
Nonlinear Dynamics and Chaos

PHYS 4267/6268  -  Spring 2006
www.cns.gatech.edu/~predrag/phys4267
TTh 9:35-10:55 Howey S204

svn: $Author: predrag $ - $Date: 2006-03-10 19:15:17 -0500 (Fri, 10 Mar 2006) $
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Course Schedule
January 10
1. A brief history of motion in time
Reading: Chapter 1; Chapter 2, sections 2.1-2.3
Optional reading: ChaosBook.org Brief history of chaos might amuse you.
January 12
2. Vector fields and flows
Reading: Chapter 2
Problem set 1: 2.1.1, 2.1.2, 2.1.3, 2.2.7, 2.2.11, 2.4.7, 2.6.1 (solutions)
January 16
Institute holiday - MLK Day
January 17
3. Bifurcations in one-dimensional systems
Reading: Chapter 3
January 19
4. Bifurcations in one-dimensional systems
Reading: Chapter 3
Problem set 2: 2.7.3, 2.8.6, 3.1.2, 3.2.2, 3.4.4, 3.5.4 (solutions)
January 24
5. Bifurcations in the presence of symmetry
Reading: Chapter 3
January 26
6. Imperfect bifurcations
Reading: Chapter 3
Problem set 3: 3.4.11, 3.5.8, 3.7.5, 3.4.12 (solutions by Daniel Borrero)
January 31
7. Flows on the circle
Reading: Chapter 4
February 2
8. Two-dimensional systems
Reading: Chapter 5, sections 5.1, 5.2
Problem set 4: 4.1.5, 4.3.1, 4.4.1, 5.1.1, 5.1.4, 4.3.2, 4.5.3 (solutions by Chris Malec)
February 7
9. Two-dimensional systems
Reading: Chapter 5, section 5.3
February 9
10. Phase plane analysis
Reading: Chapter 6, sections 6.1, 6.2, 6.3
Problem set 5: 5.1.9, 5.2.2, 6.1.2, 6.3.10, 6.1.14 (solutions by Daniel Borrero)
February 14
11. Phase plane analysis
Reading: Chapter 6, sections 6.4, 6.5, 6.6
February 16
12. Conservative Systems
Reading: Chapter 6, section 6.5
Problem set 6: 6.3.12, 6.5.8, 6.5.9, 6.5.10, 6.5.12, 6.5.19 (solutions by Chris Malec, phase portrait from problem 6.5.12, problem 6.5.10 )
February 21 - lecture by R. Grigoriev
13. Pendulum, index theory
Reading: Chapter 6, sections 6.7-6.8
February 23 - administered by R. Grigoriev
14. Midterm exam
(solution, part 1 by Domenico Lippolis)
February 28
15. Limit cycles
Reading: Chapter 7, sections 7.0-7.3
March 2
16. Relaxation oscillators
Reading: Chapter 7, section 7.5
Optional reading: ChaosBook.org chapter Get straight, section 7.3 illustrates simplification of a mechanical dynamical system by linear scalings and nonlinear time and space reparametrization.
Problem set 7: 6.7.4, 6.8.12, 7.1.6, 7.2.6, 7.5.3; the 2-d system part 2 of the midterm exam
March 7
17. Nonlinear oscillators and averaging
Reading: Section 7.6
March 9
18. Nonlinear oscillators and averaging
Reading: Section 7.6
Problem set 8: 7.5.1, 7.6.12, 7.6.14, 7.5.7, 7.6.2, 7.6.25 [pink: extra-points problem for everybody]
March 14 - lecture by R. Grigoriev
19. Bifurcations in two dimensions
Reading: Chapter 8, sections 8.1, 8.2
Problem set 8 due in class

underConstructionRest of the schedule is preliminary

March 16
20. Hopf bifurcation
Reading: Chapter 8

March 20-24
Midterm recess

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March 28
21. Global bifurcations of cycles
Reading: Chapter 8

March 30
22. Josephson junction/driven pendulum problem
Reading: Chapter 8

April 4
23. Quasiperiodicity and Poincare maps
Reading: Chapter 8

April 6
25. Quasiperiodicity and Poincare maps
Reading: Chapter 8

April 11
27. Chaos
Reading: Chapter 9

April 13
28. Chaos
Reading: Chapter 10
Matlab simulations of the Rossler system: reduction to 2D and 1D maps and stretching of phase space volumes

April 18
29. One-dimensional maps
Reading: Chapter 10

April 20
30. Universality
Reading: Chapter 10

April 25
31. Strange attractors
Reading: Chapter 12

April 27
32. Fractals
Reading: Chapter 11

Final exam (solutions)

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Friday Apr 28: classes end

grades deadline Mon, May 8

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Predrag.Cvitanovic [at] physics.gatech.edu
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