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)