Question 3. (10 points) Two species of animals compete for resources in
a National Park. Assume that the system can be modelled by the following
discrete time equations:
$$A_{n+1} = \delta_1 A_n - \delta_3 A_n B_n$$
$$B_{n+1} = \delta_2 B_n - \delta_4 A_n B_n$$
where $\delta_1$, $\delta_2$, $\delta_3$, $\delta_4$ are positive constants.
(a) Find all fixed points.
(b) Use the Jury condition to determine the stability of the fixed points
for the specific case $\delta_1 = 1.2$, $\delta_2 = 1.3$, $\delta_3 = 0.001$, and $\delta_4 = 0.002$.
