Hare-Lynx: Interactively Explore Population Dynamics

This model explores a typical predator/prey system based on Lotka–Volterra dynamics. This relatively simple system is a good way to get started with understanding population dynamics. The model requires the free SystemDynamics Modelica library, which can be downloaded from here.

To run this example, you'll need

SystemModeler 5 and Mathematica 10 or 11.

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The Model

Download the example model and see how the populations of hares and lynx affect the birth and mortality rate of each other. A high density of hares will decrease the death rate of the predator, lynx. A higher density of lynx will in turn increase the death rate of the hares. In the model, parameters such as birth factors and initial conditions can be tweaked and experimented with.
The system diagram shows how the populations of the hares and lynx affect each other.

Interactive Simulation

The included notebook uses a WSMParametricSimulate object to interactively explore the model. With the simulation object, different custom visualizations and interactions can be constructed. In the notebook, a parametric plot of the hare versus lynx population is plotted on top of a locator pane where the initial conditions can be chosen. Additional sliders allow you to change parameter values in the model.
The start values of the different animal populations can be set by moving the crosshair. The population trajectories will form a limit cycle, regardless of the initial conditions.

Create Custom Interactions

By scripting in the Wolfram Language, custom manipulation objects and visualizations can be created.

Explore the SystemDynamics Library

Use the SystemDynamics library in SystemModeler to model predator-prey interactions.