Math 410 Webpage

Lynx and Hare: predator and prey




Computer Lab information

Math Biology links

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)