In Exercises 67 and 68, species X preys on species Y. The sizes of the populations are represented by x = x(t) and y = y(t). The growth rate of each population is governed by the system of differential equations x€² = Ax + b, where

and b is a constant vector. Determine what happens to the two populations for the given A and b and initial conditions x(0). (First show that there are constants a and b such that the substitutions x = u + a and y = v + b convert the system into an equivalent one with no constant terms.)

Transcribed Image Text:

х х3 Ly. -1 10 , x(0) 40 -1 -1 30 ||