Lotka-Volterra System

The following example is taken from to introduce a very commonly discussed continuous problem: the predator-prey population interaction. In the 1920s and 1930s, Vito Volterra and Alfred Lotka independently reduced Darwin's predator-prey interactions to mathematical models.

This section presents a model of predator and prey where association includes only natural growth or decay and the preadator-prey interaction itself. All other relationships are considered to be negligible. We will assume that the prey population grows exponentially in the absense of predation, while the predator population declines exponentially if the prey population is extinct. The predator-prey interaction is modeled by mass action terms proportional to the product of the two populations. The model is named the Lotka-Volterra system.