The classic Lotka–Volterra model was originally proposed to explain variations in fish populations in the Mediterranean, but it has since been used to explain the dynamics of any predator-prey system in which certain assumptions are valid. Here, using SystemModeler, we explore the oscillations of the snowshoe hare and the lynx.
The Lotka–Volterra Model as a Component-Based Model
The Lotka–Volterra model in an intuitive component style created in Wolfram SystemModeler and Mathematica.
is a useful function in Mathematica
that makes it possible to create Modelica models in SystemModeler.
You can create standalone models, connectors, or models that extend from other models using this command. To illustrate the use of WSMCreateModel, the component "hare" in the predator-prey model was created in Mathematica.
At the top of the figure above is the Mathematica code that specifies the equations, initial equations, connectors, and parameters of the model. The output at the bottom represents the Modelica text view version of the created model.
Explore the Predator-Prey Interactions
The simulation shows how the populations of hare and lynx interact with each other. When the hare population is plentiful, there is enough prey for the lynx population to grow. As predation increases, the number of hares starts to decrease, and eventually prey becomes a limiting factor for the large population of lynxes. Play around with the model parameters to see how they influence the populations.