0).a) Show that the system can be written in dimensionless form asdx= #(1–2) – hdTfor suitably defined dimensionless quantities.b) Plot the vector fields for different values of h (show all...

Extracted text: Exercise 5. (Fishery Model) The equation N = rN(1 – ) – H represent a K simple population model of a fishery with the term -H representing a constant harvesting rate (H > 0). a) Show that the system can be written in dimensionless form as dx = #(1–2) – h dT for suitably defined dimensionless quantities. b) Plot the vector fields for different values of h (show all qualitative behaviors). c) Show that a bifurcation happens at a critical value he, determine the value, and classify the bifurcation. d) Discuss the long-time behavior of the population for h < he="" and="" h=""> he, and give a biological interpretation to both cases. e) have explored. Determine what the flaw is and advance a possible solution. (Hint: it is related to a missing fixed point) This model has a major flaw compared to other population models we