Question 16. [10 points] There is a war for survival between werewolves (L) and vampires (V) that thankfully leaves humans unaffected (phew!). Since a vampire can infect a werewolf and turn it into vampire, and vice versa, the population of these two monstrous species is modelled by the following system: dL = 100L - 5VL dt dV dt = V(100 - V) - VL (a) Find all biologically meaningful equilibrium points. (b) Show that the Jacobian is given by 100 - 5V -5L -V 100 - 2V - L (c) For each of the biologically meaningful equilibria from (a), find the eigenvalues of the Jacobian matrix. (d) Classify each equilibrium and determine its stability. (e) Draw the nullclines in the region L 2 0, V 2 0 (f) Sketch several solutions on the same graph as (e) that start in the interior (i.e., not on the axes) (g) If there are 20 vampires and 5 werewolves initially, what happens eventually