The equilibrium points occur when
If you set
and
Since the population of both is positive we reject
And solve
and
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?
Thanks!