Lotka Volterra Model
Overview
The Lotka Volterra Model is a simple model of predator and prey populations.
Lotka Volterra Equations
The Lotka Volterra equations model the populations of two species, given by {% x(t) %} and {% y(t) %}.
{% \frac{dx}{dt} = x(\lambda - by) %}
{% \frac{dy}{dt} = y(-\mu + cx) %}
{% x(t) %} represents the prey, while the predators are modeled as {% y(t) %}. Here, the prey growth rate is positively related
to the number of prey present. However, the presence of predators will negatively impact the prey growth.
The predator dies off at a constant rate in the absence of prey (their food), but the more prey present, the predator death rate
goes down, and may become positive.
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