Lynx and Hare: predator and prey
Lecture Notes (slides)
Part 1: Population models of scalar ODE
Lecture 1: Introduction
Lecture 2: Malthus model, logistic
model and separation of variables
Lecture 3: Direction field (slope
field), phase line and Euler's method
Lecture 4: Allee effect, linear regression
data fitting for Malthus and logistic models
Lecture 5: Nodimensionalization,
harvesting models
Lecture 6: Linearization and stability
of equilibria, bifurcation
Lecture 7: Case study: Spruce budworm
model
Lecture 8: Summary of Part 1, and
one more example of bifurcation
Lecture 9: Exam
Part 2: Modeling via systems
Lecture 10: Lokta-Volterra predator-prey
model, qualitative and numerical tools for planar systems
Lecture 11: Phase plane analysis
(I): nullclines, equilibrium and linearization
Lecture 12: Phase plane analysis
(II): linear planar systems, global dynamics
Lecture 13: Population models: predator-prey, competition
and coorperation
Lecture 14: Chemotaxis (I): model, nondimensionalization
Lecture 15:
Lecture 16:
Lecture 17:
Lecture 18:
Supplemental Notes
Polking's
book Chapter 3
Notes 1: Population growth
Notes 2: ODE
Notes 3: Nondimensionalization
Notes 4: Linear planar systems
Other Material
An Essay on the Principle of Population (Essay by T. Malthus)
Boom and Bust Mathematics (a webpage about P. Verhulst)
The Struggle for Existence (by Georgyi Frantsevitch Gause)
Paper on spruce budworm (by Ludwig, Jones and Holling, 1978)