Southern California Conferences for Undergraduate Research

Southern California Conferences for Undergraduate Research

Mathematical Modeling Interactions Between Human and Fish Populations: A Bio-Economic Approach

Authors:

Jared Duchen, Kimberly Vilimas

Mentor:

Joanna Bieri, Professor of Mathematics, Ph.D, University of Redlands, CA

Mathematically modeling interactions between fish and fisherman can be a powerful tool in the formulation of optimal management strategies. In our research, we utilized computer simulations in order to model a system of nonlinear recurrence relations which implement population mathematics as well as economic concepts. We then analyzed the system by means of fixed points, Jacobian stability testing, graphical interpretations, and parameter analysis using the Jury test. The main objectives of this piece are to: (i) recreate and verify the traditional pure open access bio-economic model pioneered by Gordon [1954], Scott [1955] and Schaeffer [1957] and (ii) discuss the implications these results have on the fish industry today, including what needs to be improved and updated.


Presented by:

Kimberly Vilimas

Date:

Saturday, November 17, 2012

Poster:

84

Room:

Broome Library

Presentation Type:

Poster Presentation

Discipline:

Mathematics
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