Predator-Prey Situation
A predator-prey situation occurs with two populations, when encounters be-
tween members of the populations benet the members of one population (preda-
tors) but adversely aect the members of the other population (prey). For a
simple model assume that the prey has an adequate food supply and that in the
absence of interaction there will be a positive rate of increase proportional to
the population size. The incidence interactions will depend on the size of both
populations and may be taken to be proportional to their product, and the ef-
fect will increase the rate of growth of the predator population and decrease the
rate of growth of the prey population.
Without a course in DEs, it will be hard for us to solve the pair of dierential
equations we come across, so I will help you by giving you that the equations
eventually simplify down to d2y
dt2 = Bdx
dt and d2x
dt2 =