Introduction to
Nonlinear Dynamics and Chaos
Tu,Th 9:35-10:55 Howey S204
ChaosBook.org/~predrag/courses/PHYS-4267-16/
August 23
1. Introduction
Reading: Chapter 1; Chapter 2, sections 2.1-2.3
Optional reading:
ChaosBook.org Brief history of chaos might amuse you.
Online: Strogatz lecture 1
August 25
2. Flows on the line
Reading: Chapter 2
Online: Strogatz lecture 2 up to minute 34
Fun stuff:
snowflakes
Problem set #1: 2.1.5, 2.2.10, 2.3.3, 2.4.2, 2.4.9
(click here)
August 30
3. Experimental nonlinear dynamics
Reading: Chapter 2
Presentation: CRAB lab -
Will Savoie, Andy Karsai and Dan Goldman
September 1
4. Numerical solution of nonlinear ODEs
Due in class: Homework #1
(for homework solutions, go to t-square, links above)
Reading: Chapter 2:
Reading:
Sections
16.0-16.3 of Numerical Recipes by Press et al.
Problem set #2: 2.5.3, 2.7.6, 2.8.3
(for solutions, go to t-square)
Note:
There is a typo in 2.8.3 part (c): you are to plot ln(E) vs. ln(Delta t).
Explain how the slope is related to the order of the method.
September 6
5. Bifurcations in one-dimensional systems I
Reading: Chapter 3
Online: Strogatz lecture 2, starting at minute 34
September 8
6. Bifurcations in one-dimensional systems II
Due in class: Homework #2
(remember, always due next Thursday)
Reading: Chapter 3
Online: Strogatz lecture 3
Online: Strogatz lecture 4
Problem set 3: 3.1.3, 3.2.6, 3.3.1, 3.4.8, 3.5.7
September 13, guest lecturer Prof. F. Fentonstein
7. Flows on a circle
Reading: Chapter 4
Fun stuff:
fireflies
and mosquitos synchronization
September 15, guest lecturer Prof. F. Fentonstein
8. Two-dimensional systems
Reading: Chapter 5
Online: Strogatz lecture 5
Problem set 4: 3.6.2, 3.7.6, 4.1.8, 4.3.7, 4.6.3
September 20
9. Phase plane analysis
Reading: Chapter 6
Online: Strogatz lecture 6
September 22
10. Conservative systems
Reading: Chapter 6
Problem set 5: 5.1.10, 5.2.13, 6.1.3, 6.2.1, 6.3.1, 6.4.7
Online: Strogatz lecture 7
September 27
11. Index theory. Limit Cycles
Reading: Chapter 7
Online: Strogatz lecture 8
September 29
12. No periodic orbits? Perturbation theory
Reading: Chapter 7
Problem set 6: 6.5.10, 6.6.3, 6.7.2, 6.8.5, 6.8.7
Online: Strogatz lecture 9
Online: Strogatz lecture 10
October 4
13. Nonlinear oscillators and averaging
Optional reading: Bender and Orszag Chapter 7
Online: Strogatz lecture 11
October 6
14. Bifurcations in two dimensions
Reading: Chapter 8
Prof. Flavio Fenton: temporal Belousov-Zhabotinsky demonstration
Problem set 7: 7.1.6, 7.2.9, 7.3.9, 7.4.1. Due October 20.
Chris says: use a computer to do plots - in the long run,
it is faster, and it's what you need to learn anyhow.
Online: Strogatz lecture 12
October 10-11
Fall break
October 13
Mid-term exam
9:35-10:55 Howey S204; see instructions
October 18
15. Hopf bifurcation
Reading: Chapter 8
Storgatz bores you? Optional ChaosBook.org
reading (none of this will be on the final):
Section 4.3 A linear diversion,
Example 4.3 Linear stability of 2-dimensional flows,
Example 4.4 In-out spirals,
Section 5.1 Equilibria,
Appendix C.2 Eigenvalues and eigenvectors.
Online: Strogatz lecture 13
October 20
16. Global bifurcations of cycles
Reading: Chapter 8
Due in class: Homework #7
Prof. Flavio Fenton: Belousov-Zhabotinsky spirals demonstration
Problem set 8: 7.5.4, 7.6.3, 7.6.6, 7.6.17
Online: Strogatz lecture 14
October 25
17. Quasiperiodicity and Poincare maps
Reading: Chapter 8
October 27
18. Floquet Theory
Reading: Chapter 8
Optional reading: Nonlinear Dynamics 1: Geometry of Chaos, week 2
Problem set 9: 8.1.8, 8.1.11, 8.2.1, 8.2.9, 8.3.1
November 1
19. Lorenz equations
Reading: Chapter 9, skip Sect 9.1 A Chaotic Waterwheel
(Malkus and Howard were my friends, but this is not the why Lorenz work was so great!)
Reading: Chapter 9, R. Grigoriev notes
Optional reading: Nonlinear Dynamics 1: Geometry of Chaos, week 1
Online: Strogatz lecture 17
Numerical exploration of different dynamical regimes (: Maple! :)
November 3
20. Lorenz equations
Reading: Chapter 9
Problem set 10: 8.4.2, 8.4.12, 8.5.2, 8.6.1, 8.7.5
Bonus problem set 10+: Geometry of Chaos, homework 1
(email me the grade sent to you by the autograder)
Online: Strogatz lecture 18
November 8
21. One-dimensional maps
Reading: Chapter 10
Optional reading: Nonlinear Dynamics 1: Geometry of Chaos, week 7
Optional: Matlab simulations of the Rossler system:
reduction to 2D and 1D maps and
stretching of phase space volumes
Online: Strogatz lecture 19
November 10
22. Universality
Reading: Chapter 10, R. Grigoriev lecture notes
Optional reading,
ChaosBook.org bootleg chapters: Universality in transitions to chaos and Complex universality
Problem set 11: assignment
Online: Strogatz lecture 20
November 15
23. Charting the state space
Reading:
ChaosBook.org, Chapter 14 and Chapter 15, edited for PG-13
Optional viewing: Nonlinear Dynamics 1: Geometry of Chaos, week 7
November 17
24. Kneading theory
Reading: Chapter 11, Sect. 11.2 (rest mostly useless 1980's flounderings)
Fractals in
nature,
biology, and
mathematics.
Problem set 12: 10.1.11, 10.2.6 (see comments for 10.2.3),
10.3.11, 10.4.1 - due December 1
November 22
25. Learning how to count
Reading:
ChaosBook.org,
Chapter 17 and Chapter 18, edited for PG-13
Optional viewing: Nonlinear Dynamics 1: Geometry of Chaos, week 9
Optional reading:
Aligood, Sauer, and Yorke
Problem set 13: assignment - due December 1
November 24
Holiday
November 29
26. Learning how to measure
Reading:
ChaosBook.org,
Chapter 19 and Chapter 20, edited for PG-13
Optional viewing: Nonlinear Dynamics 1: Geometry of Chaos, week 10
December 1
27. Ah, chaos!
December 6
28. Wrapping it all up; overture
Reading:
ChaosBook.org,
Chapters 21 to 23, edited for PG-13
Optional viewing: Nonlinear Dynamics 1: Geometry of Chaos, week 11
December 8
Final exam
2:50-5:40pm Howey S204; see instructions