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6-020-AlgaePopulationSelf-Replenishment-ModelingScenario

Author(s): R. Corban Harwood

George Fox University

Keywords: algae population Mexico qualitative compartment linearization Jacobian lak nondimensionalization pplane

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Abstract

Resource Image This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. A

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

After reading a summary of news articles on the incident, students create an ODE system model from a verbal description of the factors, visualize this system using an executable Java applet (PPLANE) to predict overall behavior, and then analyze the nonlinear system using the Jacobian matrix, eigenvalues, phase plane, and feasibility conditions on parameters to fully describe the system behavior. Students are expected to be familiar with systems of differential equations, equilibria, jacobian matrices, and eigenvalues. Students will learn modeling from qualitative descriptions, nondimensionalization, applying feasibility conditions to parameters, and how to use technology to interactively analyze a system of differential equations.

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Authors

Author(s): R. Corban Harwood

George Fox University

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