Differential equations allow us to mathematically model quantities that change continuously in time. One of the simplest examples of a changing quantity is the number of plants or animals of a particular species. Although populations are discrete quantities (that is, they change by integer amounts), it is often useful for ecologists to model populations by a continuous function of time. Modeling can predict that a species is headed for extinction, and can indicate how the population will respond to intervention.

Populations grow according to the number of individuals that are capable of reproduction. At the same time, their growth is limited according to scarcity of land or food, or the presence of external forces such as predators. In this module, we examine simple differential equations that model populations. We also introduce and explore powerful techniques for the geometric analysis of differential equations: phase space, equilibria, and stability.

- The Main Ideas of the Module
- Unbounded Populations
- Limits on Growth
- Equilibria, Stability, and Phase Space
- Harvesting
- Conclusion

Support for the Curriculum Initiative Project at the University of Minnesota has been provided by a grant from the National Science Foundation (DUE 9456095) and by the Geometry Center.

Comments to:
webmaster@geom.umn.edu

Created: May 15 1996 ---
Last modified: May 15 1996

Copyright © 1996 by
The Geometry Center
All rights reserved.