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Modeling Scenario

6-022-CannibalismPredatorPrey-ModelingScenario

Author(s): Evan Cowden1, Maila Hallare1

United States Air Force Academy, USAFA CO USA

Keywords: stability predator-prey equilibria oscillations cannibalism phase planes spiral sinks

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Abstract

Resource Image The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time. In this module, we look at modifying this prey-predator model to consider the case when there is cannibalism in the predator species.

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Description

The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time.

In this module, we look at modifying this prey-predator model to consider the case when there is cannibalism in the predator species. Cannibalism has been observed when the resource pool becomes limited. This complicated interaction between the cannibalistic predator and the prey can be analyzed using mathematical modeling via Ordinary Differential Equations (ODEs).

This investigation includes performing equilibrium, stability, and nullcline analyses, and a careful plotting of the phase plane. Fortunately, there is a free software, PPlane, that helps in producing phase planes to analyze the dynamics between the predator and the prey when the cannibalism rate of the predator increases and the growth rate of the prey decreases and hence cannibalism increases.

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Authors

Author(s): Evan Cowden1, Maila Hallare1

United States Air Force Academy, USAFA CO USA

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