Math 441 Schedule

 

Date

Sections

Lecture

Homework

Other readings

Software

9/1(R)

1.0-1.3

Lecture 1

 HW1 pdf

(due Sept 9)

Wolfram Alpha
Dynamical systems
Lorenz Equation

 

9/6(T)

2.0-2.4

Lecture 2

Noy-Meir Jour Ecology 1975
Solow Quart Jour Econ 1956

 

9/8(R)

2.5-2.8

Lecture 3


Proof of Existence-Uniqueness

 

Contraction mapping theorem

Matlab programs: graph2 graph3
logistic ode logistic ode (multi)

 

Direction field plotter

9/13(T)

3.0-3.2

Lecture 4

HW2 pdf

(due Sept 17)

Bifurcation   Buckling
Swat Bioinformatics 2004
Scheffer Nature 2001

 

9/15(R)

3.2

 

 

9/20(T)

3.3-3.4

Lecture 5

Nondimensionalization

HW3 pdf

(due Sept 27)

Bead on a rotating wire video

9/22(R)

3.5-3.7

Lecture 6

 

Ludwig Jour Anim Ecol 1978

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

9/27(T)

3.6, 5.0-5.2

Lecture 7

planar linear equation

HW4 pdf

(due Oct 4)

Catastrophe theory
cusp bifurcation

differential equation on youtube

9/29(R)

5.3, 6.0-6.3

Lecture 8

Project guide

Phase portrait plotter

Linear system plotter

10/4(T)

6.4

Lecture 9

Competition

HW5 pdf

(due Oct 10)



 

10/6(R)

6.5-6.6

Lecture 10

 

10/11(T)

6.6-6.7

Lecture 11

HW6 pdf

(due Oct 24)

 

10/13(R)

Fall Break

No class

 

 

 

 

Date

Sections

Lecture

Homework

Other readings

software

10/18(T)

6.7-6.8

Lecture 12

 

Hamiltonian system

 

10/20(R)

7.1-7.2

Lecture 13

a video of oscillatory chemical reaction
Halloween clock reaction

10/25(T)

7.2-7.3

Lecture 14

HW7 pdf

(due Nov 1)

periodic orbit

10/27(R)

7.3-7.6

Lecture 15

Van der Pol oscillator

Van der Pol equation

11/1 (T)

8.1

Lecture 16

HW8 pdf

(due Nov 8)

Gray-Scott model
Klausmeier, Science, 1999

11/3 (R)

8.2

Lecture 17

Hopf bifurcation
Rosenzweig 1971 Science

11/8(T)

8.3

Lecture 18

HW9 pdf

(due Nov 15)

Lengyel-Epstein, Science 1991
Belousov Zhabotinsky chemical reaction

11/10(R)

4.1-4.3, 8.4, 8.6

Lecture 19



11/15(T)

9.0-9.4

Lecture 20

HW10 pdf

(due Nov 29)

Routh-Hurwitz criterion

Harvard water wheel
Edward Lorenz
Lorenz attractor

lorenz.m
foodchain.m

rossler.m

Strogatz's watewheel video

Lorenz video

Harvard waterwheel video

11/17(R)

11/22(T)

9.0-9.4

Strogatz water wheel 1

Strogatz water wheel 2

11/24(R)

Thanks

giving

No class

11/29 (T)

10.0-10.3

 

HW11 pdf

(due Dec 6)

May Nature 1976

logistic map

malthus.m

sine.m

cobweb_sine.m

cosine.m

cobweb_cosine.m
logistic.m
cobweb_logistic.m

12/1(R)

10.0-10.3

Lecture 21

bifurcation_logistic.m
bifurcation_sin.m

12/6(T)

10.4-10.6

Lecture 22

List of chaotic maps, chaos
period 3 implies chaos (Li, Yorke, 1975, Amer Math Mon)

Sharkovskii’s theorem
birth of period 3 (Saha, Strogatz, 1994, Math Magazine)

12/8(R)

11.0-11.3

Lecture 23

Fractal  self-similar  list of fractal 
Cantor set
Koch snowflake

koch.m
kochstep.m

12/12(M)

2-5pm

presentation

 

 

 


Oscillatory Chemical reaction: Oregonator, Brusselator, Belousov-Zhabotinsky reaction

 

Possible topics of project:

Physics:

1.      Van der Pol oscillator (Eric)

2.     Duffing Oscillator (Nick)

3.     3 body problem (John)

4.     Double pendulum (Patrick)

Economics:

5.      Kaldor's business cycle model

6.      Hopf bifurcation in an advertising diffusion model

Biology:

7.      Bifurcation analysis in a bioinformatics model

8.      Bistability in coral reef model (Yi-Cheng)

9.     Backward bifurcations in simple vaccination models

10. Harvesting in a Lotka-Volterra competition model (Jarred)

11. Forest-savanna dynamics (Gwendolyn)

12. Destabilizing effect of cannibalism on a structured predator-prey system (Sam)

Chemistry

13. Autocatalytic chemical reaction: Hopf bifurcation and multistability

14.  Smallest chemical reaction system with Hopf bifurcation

15.  Smallest chemical reaction system with bistability

16.  Oregonator (Katherine)

Other

17.  Modeling the love story in “Gone with the wind” (see also problem 7.2.19)

18.  Threshold Linear Network Models of Neural Networks (Luke)