Chapter 9.6, Problem 2E

Each system of differential equations is a model for two species that either compete for the same resources or cooperate for mutual benefit (flowering plants and insect pollinators, for instance). Decide whether each system describes competition or cooperation and explain why it is a reasonable model. (Ask yourself what effect an increase in one species has on the growth rate of the other.)

(a) $\begin{array}{l}\frac{dx}{dt}=0.12x-0.0006x^2+0.00001xy\\ \frac{dy}{dt}=0.08x+0.00004xy\end{array}$

(b) $\begin{array}{l}\frac{dx}{dt}=0.15x-0.0002x^2-0.0006xy\\ \frac{dy}{dt}=0.2y-0.00008y^2-0.0002xy\end{array}$