The equilibrium points occur when
If you set
Since the population of both is positive we reject
This gives the desired conclusion.
From the following equations, set at a fixed positive value. Show that as , the equilibrium point inside the population quadrant approaches the point on the y-axis and that if
H2 = c, all points on the y-axis are equilibrium points of system (9).
I decided to let H1 = 1.
It would seem that as , the equation would reduce to .
I don't know how to solve for the equilibrium point, however.
The only mention in my book I find is the following excerpt:
"If the harvest coefficients in the above 2 equations are too large, the internal equilibrium point crosses the positive y-axis, and one (or both) species becomes extinct, as we see in the next example."
Where should I start in proving the equilibrium point?