A herd of fish-cating dinosaur, Suchomimus tenerensis, lived near a lake in Africa in the Cretaceous period. Suppose that the dinosaur population of size N(t) grows logistically, with carrying capacity proportional to the population of the fish F(t) in the lake, while F(t) also grows logistically (with constant carrying capacity), but is depleted by predation at a rate proportional to both F and N. (a) Write down a set of differential equations describing the populations of dinosaur N(t) and fish F(t), and explain the model assumptions. (b) Show that a non-dimensional form of the model can be written as du dT " = Bu (1 -") , (2) du dT = v(1 -v) - Quv, v70 where N = N*u, F = F*v, t = (*7, and F"*, N* and f* have to be determined. Find the parameters o and B