Chapter 12.3, Problem 23E

To determine

(a)

To find:

The carrying capacity of $x$.

To determine

(b)

To find:

Carrying capacity of $y$.

To determine

(c)

To show:

The system can be rewritten in the equivalent form

$\frac{dx}{dt}=a_{1}x\left(1-\frac{x}{A}-\frac{d_{1}y}{A}\right)$,

$\frac{dy}{dt}=a_{2}y\left(1-\frac{y}{B}-\frac{d_{2}x}{B}\right)$,

Here, $d_i=c_i/b_i,i=1,2$, and $A$ and $B$ denote the carrying capacity for species $x$ and $y$.

To determine

(d)

To describe:

The competing populations if the application of the insecticide is increased (that is, $a_1$ is decreased).