Competing Species
Consider an ecosystem consisting of two species which compete for a common food
supply. Denote by y1 (t) and y2 (t) the sizes of the two populations at time t. If food is
plentiful, then each member of population number i causes, on average, a net increase of
bi per unit time in the size of its population. That is
dyi
dt (t)
= bi yi (t). As the sizes of the
populations grow the amount of food available per member decreases and consequently the
net birthrates also decrease, say to b1 −f1 y1 (t)−g1 y2 (t) and b2 −g2 y1 (t)−f2 y2 (t) respectively.
Hence
c Joel Feldman.
dy1
dt
= b1 y1 − f1 y12 − g1 y1 y2
dy2
dt
= b2 y2 − g2 y1 y2 − f2 y22
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