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 16)	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 23)		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 Sept 30)	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 7)
10/6(R)	6.5-6.6	Lecture 10		Hamiltonian system
10/11(T)	6.6-6.7	Lecture 11	HW6 pdf (due Oct 14)
10/13(R)	Fall Break	No class

Date	Sections	Lecture	Homework	Other readings	software
10/18(T)	6.7-6.8	Lecture 12
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)	Election day	No class	HW9 pdf (due Nov 15)	Lengyel-Epstein, Science 1991 Belousov Zhabotinsky chemical reaction
11/10(R)	8.3	Lecture 18
11/15(T)	4.1-4.3, 8.4, 8.6	Lecture 19	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)	9.0-9.4	Lecture 20		May Nature 1976 logistic map	malthus.m sine.m cobweb_sine.m cosine.m cobweb_cosine.m logistic.m cobweb_logistic.m
11/22(T)	10.0-10.3	Lecture 21			Strogatz water wheel 1 Strogatz water wheel 2
11/24(R)	Thanks giving	No class
11/29 (T)	10.4-10.6	Lecture 22	HW11 pdf (due Dec 6)	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)	bifurcation_logistic.m bifurcation_sin.m
12/1(R)	11.0-11.3	Lecture 23		Fractal self-similar list of fractal  Cantor set Koch snowflake	koch.m kochstep.m
12/6(T)	presentation
12/8(R)	presentations

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

Possible topics of project:

Physics:

1. Van der Pol oscillator

2. Duffing Oscillator

Economics:

3. Kaldor's business cycle model

4. Hopf bifurcation in an advertising diffusion model

Biology:

5. Bifurcation analysis in a bioinformatics model

6. Bistability in coral reef model

7. Backward bifurcations in simple vaccination models

8. Harvesting in a Lotka-Volterra competition model

9. Forest-savanna dynamics

10. Destabilizing effect of cannibalism on a structured predator-prey system

Chemistry

11. Autocatalytic chemical reaction: Hopf bifurcation and multistability

12. Smallest chemical reaction system with Hopf bifurcation

13. Smallest chemical reaction system with bistability

14. Oregonator

Other

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