To model the behaviour in a predator–prey situation, the normal dependencies on birth and death rates for each population are modified by terms reflecting the species’ interdependency: since the rate of encounter between predator and prey is approximately proportional to the product of the population sizes, this would give rise to linked differential equations of the form

These equations are also known as the Lotka–Volterra equations after Alfred Lotka and Vito Volterra who independently introduced them. There is an unstable equilibrium at X = Y = 0 and a single stable equilibrium at non-zero X and Y.

http://home.messiah.edu/~deroos/CSC171/PredPrey/PPIntro.htm Simulations of fox and rabbit populations.