Lynx and Hare: predator and prey
Mathematical Biology Links Links by Eduardo Sontag Links by Kuang Yang Links by Josef Hofbauer
Mathematical
Biology Journals in College of William and Mary library and network
Schedule
| Date |
Sections |
Content |
Lecture Notes |
Computer program |
Homework |
| 8/31 (Th) |
1.1 |
Introduction |
Lecture
1 |
||
| 9/5 (Tu) |
1.2, |
Single species population
dynamics (discrete time) |
Lecture 2 |
malthus.m
wildebeest.m cobweb_hassell.m |
|
| 9/7 (Th) |
1.2, A.1 |
Linearization, |
Lecture 3 |
plot_bellows.m
cobweb_bellows.m bifurcation_bellows.m bifurcation_bellows_2.m |
Homework 1 |
| 9/12 (Tu) |
A.2 |
Bifurcation, | Lecture 4 |
||
| 9/14 (Th) |
1.3, B.1 |
Single species population dynamics (continuous time), | Lecture 5 |
Homework 2 |
|
| 9/19 (Tu) |
B.1 |
phase line, linearization, |
Lecture 6 |
dfield7.m
us_pop.m us_pop_2.m graph.m |
|
| 9/21 (Th) |
B.4.1 |
Nondimensionalization,
bifurcation |
Lecture 7 |
notes on
nondimensionalization |
Homework 3 |
| 9/26 (Tu) |
1.5 |
Harvesting, spruce budworm model |
Lecture 8 |
||
| 9/28 (Th) |
1.6 |
Metapopulation |
Lecture 9 |
matrixcalculation.m
graphing.m |
Homework 4 |
| 10/3 (Tu) |
1.8 |
Fibonacci's rabbit, matrix model |
Lecture 10 |
moving.m |
|
| 10/5 (Th) |
A.3, D.1 |
Eigenvalue and eigenvector | Lecture 11 |
stage.m
eigen1.m us_pop_hw4.m |
Midterm exam
1 |
| 10/10 (Tu) |
1.9 |
Leslie Matrix model |
Lecture 12 |
loggerhead.m
loggerhead_1.m loggerhead_2.m loggerhead_3.m |
paper
on loggerhead population |
| 10/12 (Th) |
1.10 |
Euler Lotka equation |
Lecture 13 |
||
| 10/17 (Tu) |
no class, fall break |
| Date |
Sections |
Content |
Lecture Notes |
Computer Program |
Homework |
| 10/19(Th) |
2.3, B.2.1 |
predator-prey, phase plane
analysis |
Lecture 14 |
pplane7.m |
Homework 6 |
| 10/24(Tu) |
B.2.2 |
linearization |
Lecture 15 | whooping_crane.m
midterm_3.m |
solution
of test1 |
| 10/26(Th) |
2.5, 2.3 |
competition, predator-prey |
Lecture 16 | ||
| 10/31(Tu) |
2.3, 2.4 |
predator-prey, limit cycle |
Lecture 17 | Homework 7 |
|
| 11/2(Th) |
3.1, 3.2, |
epidemics |
Lecture 18 | ||
| 11/7(Tu) |
3.3, 3.4 |
epidemics |
Lecture 19 | ||
| 11/9(Th) |
4.1, 4.2, 4.3 | genetics |
Lecture 20 |
sir.m predatorprey.m hopf.m |
|
| 11/14(Tu) |
4.4, 4.5 |
genetics |
Lecture 21 |
midterm exam
2 |
|
| 11/16(Th) |
6.4 |
nerve conduction, action
potential |
Lecture 22 |
||
| 11/21(Tu) |
6.2,6.3 |
enzyme kinetics |
Lecture 23 |
||
| 11/23(Th) |
Thanksgiving holiday |
||||
| 11/28(Tu) |
5.2, 5.3 |
diffusion |
Lecture 24 |
malthus-diffusion.mws |
|
| 11/30(Th) |
5.6 |
traveling wave |
Lecture 25 |
traveling-wave-fisher.mws |
|
| 12/5(Tu) |
project presentation |
||||
| 12/7(Th) |
project presentation |
||||
| 12/13(Wednesday) |
project paper due |
| Name |
Project topic |
Presentation time |
| Edward |
age-structured
predator-prey
model |
12/5 |
| Janet |
antibody binding |
12/5 |
| Stavros |
impact
of biodiversity on
epidemics |
12/5 |
| Trevor |
Island
bird ecology |
12/5 |
| Rennie |
Anthropology: model of
emigration and genetic evollution of human |
12/5 |
| Rachel |
Migration of birds |
12/5 |
| Natalie |
Pest control model |
12/5 |
| Katie |
Tumor
modeling |
12/7 |
| Juliann |
population-resource modeling |
12/7 |
| Amelia |
Neuron science model |
12/7 |
| Patrick |
Pattern formation |
12/7 |
| Connie |
neuronbiology model, lecar.ode, ican_2cell2_w_par.ode |
12/7 |
| Courtney |
Epidemics model and
2006 Iowa mumps outbreak |
12/7 |
| Tristan |
Population
of Virginia black
bears |
12/7 |
Matlab tutorial
A tutorial from Rice University
A tutorial
from University of Utah
Some Classical Papers of Mathematical Biology
An Essay on the Principle of Population (Thomas Malthus, 1798)
The
Struggle
for Existence (Georgyi Frantsevitch Gause, 1934)
Analytic
note on certain rhythmic relations in organic systems (Alfred
Lotka, 1920)
General Articles in Mathematical biology
Modeling
of Biological Systems, A Workshop at the National Science
Foundation
in 1996
Mathematics, Biology, and Physics: Interactions and
Interdependence
Michael C. Mackey and Moisés Santillán, Notices of American
Mathematical
Society, Sept, 2005.
Why Is Mathematical Biology So Hard? Michael C. Reed, Notices of American Mathematical Society, March, 2004.
Uses and
Abuses of Mathematics
in Biology Robert M. May,
Science,
February 6, 2004.
A
webpage about Brahe, Kepler and Newton's story
Mathematical Challenges from Genomics and Molecular
Biology
Richard M. Karp, Notices of American
Mathematical
Society, May, 2002.
Mathematical Challenges in Spatial Ecology
Claudia Neuhauser, Notices of American
Mathematical
Society, Dec. 2001.
Linking Mind to Brain: The Mathematics of Biological
Intelligence
Stephen Grossberg, Notices of American
Mathematical
Society, Dec. 2000.
We Got Rhythm: Dynamical Systems of the Nervous System Nancy Kopell, Notices of American Mathematical Society, Jan. 2000.
Getting Started in Mathematical Biology Frank Hoppensteadt, Notices of American Mathematical Society, Sept. 1995.
Some Advice to Young Mathematical Biologists Kenneth Lange, (from internet), date unknown.
How the leopard gets its spots? James Murray, Scientific American, 258(3): 80-87, 1988.