One of the most well-known mathematical models in ecology is the Lotka-Volterra predator-prey system of differential equations. Initially, this model was used to analyze interactions between two animal populations. But ecologists discovered that it could also be applied to plant (`prey') and herbivore (`predator') interactions. A grazing system (such as sheep in a pasture) is a special type of plant-herbivore system in which the herbivore population is controlled by humans. Because the number of herbivores does not change, the model consists of a single differential equation for the vegetation. In this activity, students will apply graphical analysis (such as phase lines) to determine the long-term predictions of a differential equation model for pasture grass using two different formulas for the herbivore consumption rate.
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