Math 441 Schedule



Date

Sections

Homework

Other readings/software

8/29(R)

1.0-1.3, 2.0-2.3

 

Wolfram Alpha
Dynamical systems
List of dynamical systems topics
Lorenz Equation

9/3(T)

2.4-2.5

Homework 1:  2.1.1, 2.1.2, 2.1.3, 2.2.3, 2.2.9, 2.3.4, 2.4.4, (due 9/6 F)
solution            (use Matlab to do 2.3.4 c) with r=b=1, a=2

Noy-Meir Jour Ecology 1975
Solow Quart Jour Econ 1956

9/5(R)

2.6-2.8


Matlab programs: graph1 graph2 dfield8 pplane8
logistic ode logistic ode (multi)

9/10(T)

existence and uniqueness Homework 2: pdf file  (due 9/13 F)
solution
metric space
contraction mapping theorem
existence and uniqueness proof

9/12(R)

3.0-3.1


Bifurcation   Buckling
Swat Bioinformatics 2004
Scheffer Nature 2001

9/17(T)

3.1 Homework 3: pdf file  (due 9/20 F)
solution
Jordan-Cooley Jour Theo Biol 2011

9/19(R)

3.2-3.3

 

Matlab programs: bifurcation 1, bifurcation 3
bifurcation diagram from Matlab

9/24(T)

nondimensionalization
3.4
Homework 4: pdf file (due 9/27 F)
solution
Ludwig Jour Anim Ecol 1978
Bead on a Rotating Wire

9/26(R)

3.5-3.7

 

Catastrophe theory
cusp bifurcation differential equation on youtube

10/1(T)

5.0-5.3
project guide
Homework 5: 3.6.2(a,b), 5.2.1, 5.2.2, 5.3.4, 5.3.6 (due 10/4 F)
solution
pplane (online)
planar linear equation notes (from Math 302)

10/3(R)

6.0-6.4



10/8(T)

6.5-6.7

Homework 6: 6.1.4, 6.1.10(use pplane), 6.3.6, 6.3.8, 6.3.10 (due 10/11 F)
solution
planar nonlinear system notes (from Math 302)

10/10(R)

n-body problem



10/15(T)

Fall Break

no class



Date
Sections
Homework
Other readings
software

10/17(R)

no class

Take-home midterm exam 1 (due 10/21 M 5pm) solution



10/22(T)

n-body problem
Homework 7: 7.1.5, 7.2.1, 7.2.2, 7.2.7, 7.2.10 (due 10/28 M)
solution
n-body problem 2-body problem 3-body problem
3-body problem
AMS article Xie's page Poincare

10/24(R)

7.1-7.2


periodic orbit

10/29(T)

7.3-7.4

Homework 8: 7.2.15, 7.3.1, 7.3.3, 7.4.2 (due 11/1 F)
solution

van der Pol trapping region
periodic orbit theorems
a video of oscillatory chemical reaction
Halloween clock reaction

10/31(R)

7.4, 8.1


Gray-Scott model
Klausmeier, Science, 1999

11/5(T)

8.2-8.3

Homework 9: pdf file (due 11/8 F)
solution

Hopf bifurcation
Rosenzweig 1971 Science

11/7(R)

8.3-8.4


Lengyel-Epstein, Science 1991
Belousov Zhabotinsky chemical reaction
Briggs–Rauscher oscillating reaction
predator-prey.m
myPP.m

11/12(T)

9.0-9.4
Homework 10: pdf file (due 11/15 F)
solution
A survey paper of BZ reaction (by a high school student)
Belousov-Zhabotinsky reaction
Routh-Hurwitz criterion
Strogatz's watewheel video
lorenz.m
myLorenz.m
foodchain.m
myFoodchain.m

11/14(R)

10.0-10.2


Lorenz, J.Atmo.Sci, 1963 Edward Lorenz
Lorenz attractor
Hastings-Powell-1991-Ecology
May Nature 1976
malthus.m
logistic.m
cobweb.m
cobweb_logistic.m

11/19(T)

10.3-10.4
Homework 11: 10.1.11, 10.2.6, 10.2.8, 10.3.6 (due 11/22 F)
solution
List of chaotic maps, chaos
period 3 implies chaos (Li, Yorke, 1975, Amer Math Mon)
birth of period 3 (Saha, Strogatz, 1994, Math Magazine)
two more articles:   one   two
bifurcation_logistic.m
bifurcation_bellows.m
bifurcation_sin.m

11/21(R)

11.1-11.4
Exam 2
logistic map fractal  self-similar  list of fractal  Mitchell Feigenbaum
Feigenbaum, 1978, J Stat Phys
Dynamical system Game of life
koch.m
kochstep.m

11/26(T)

project working day


rossler.m
myRossler.m
11/28(R)
no class
Thanksgiving


12/3(T)

presentations

student presentation: Jennifer, Jamie, Joe, Frank, Brooks



12/5(R)

presentations
student presentation: Isabelle, Rachelle, Leslie, Oscar, Aaron


12/6(F)

Project report due at 5pm


12/13(F)


Exam 2 due at 5pm




Oscillatory Chemical reaction: Oregonator, Brusselator, Belousov-Zhabotinsky reaction
Possible topics of project:
  1. FitzHugh-Nagumo model in neural science  (original paper in 1961) (neuron science)
  2. Van der Pol oscillator (physics) Oscar
  3. Canard explosion (mathematics) Leslie
  4. Smallest chemical reaction system with Hopf bifurcation (chemistry)
  5. Smallest chemical reaction system with bistability (chemistry)
  6. Bifurcation analysis in a bioinformatics model (bioinformatics) Brooks
  7. Bistability in coral reef model (ecology) Joe
  8. Unraveling Complex Systems (several project ideas) Isabelle
  9. Backward bifurcation in epidemic model (epidemiology)
  10. Two-body problem in general relativity (see problem 6.5.7 in Strogatz) (physics)
  11. Fireflies (Strogatz section 4.5) (physics)
  12. Josephson Junction (Strogatz section 4.6) (physics)
  13. Kaldor's business cycle model (economics) Jamie
  14. Hopf bifurcation in an advertising diffusion model, Feichtinger, 1992 Journal of Economic Behavior & Organization (economics)
  15. Hysteresis and bistability in the activation of Cdc2 (biochemistry)
  16. A simple bistable model for reforestation in semi-arid zones, or how to turn a wasteland into a forest (ecology) Rachelle
  17. Morris-Lecar model (neuron science) Jennifer
  18. Love Dynamics Frank