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03brud~1.htm Introduction to Predator-Prey Models Using TI-82, MathCad and Stella
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"Introduction to Predator-Prey Models
Using TI-82, MathCad and Stella
Phyllis Brudney and Harrell Rentz
Abstract
This project will enable the student to explore mathematical modeling through the idea of closed ecological systems. To begin the modeling process, the student will research such systems and draw diagrams of them. The purpose of this is to promote general interest in the activities by allowing students to think about models which are of particular interest to them. Since most systems are very complicated, this project will use a simple predator-prey model, foxes and rabbits, to show how mathematical models are built. The project will also expose the student to a variety of technological tools in an elementary step-by-step manner designed for the beginner. The student will experiment with the TI-82 calculator, MathCad (v3.1), and Stella II (v2.2.2) using the predator-prey model. [Earlier software versions may work also.] To conclude the project, students will write essays describing approaches they would use to model their original ecosystems.
Sequence of Activities
PART I: 1) Groups brainstorm on types of ecosystems
2) Groups pick one system of interest to research
3) Groups list variables affecting the ecosystems
4) Groups develop a diagram to model the system
PART II: Introduce simple predator-prey model: Foxes and Rabbits
PART III: Develop and explore the foxes and rabbits model using each of the following:
1) TI-82 2) MathCad 3) Stella
PART IV: 1) Groups analyze data from explorations
2) Groups write essay on how they would model the original ecosystem
3) Extension: groups actually model their original ecosystem
Activities - Part I (Group Research and Diagrams):
The teacher should lead a discussion of how ecosystems work in general, choosing one or two examples, generating a list of variables affecting the system, and drawing a flow chart. For example, the teacher might discuss "
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