Chapter 9.1, Problem 42E

Consider the interaction of two species of animals in a habitat. We are told that the change of the populations $x(t)$ and $y(t)$ can be modeled by the equations

$\left|\begin{array}{c}\frac{dx}{dt}=1.4x-1.2y\\ \frac{dx}{dt}=0.8x-1.4y\end{array}\right|$

where time t is measured in years.
a. What kind of interaction do we observe (symbiosis, competition, or predator−prey)?
b. Sketch a phase portrait for this system. From the nature of the problem, we are interested only in the first quadrant.
c. What will happen in the long term? Does the outcome depend on the initial populations? If so, how?