The 2-dimensional Lotka-Volterra system depicts the populations change of a class of predators and a class of preys. The growth rate of preys’ population over time is given by wherein are constant parameters and is the population of predators. It gives that the number of preys grows exponentially without predation. The population growth of predators is governed by the differential equation wherein are constant parameters. We set those parameters as , , and .
We consider the initial set .