question one

1. Consider the following model for sheries: (IN N where the parameters 1', K, and H are all positive. (a) What are the dependent variables and what are the independent variables? Ex- plain what each variable represents? (b) Very briey explain what each of the three parameters in this model represents- (c) Determine all equilibria. Provide a verbal interpretation for the condition required to have at least one positive equilibrium. (d) Show that the DE can be written in the form: dzr E = r (1 am) for suitany dened parameters 1', r, and a. Make sure to write down these denitions. (e) Plot % versus N for eqn.(1). Mark the equilibria on the gure appropriately. (f) Using the above gure, give graphical arguments that determine the stability properties of the equilibria. (g) Sketch the bifurcation diagram of Equation (1) for the control parameter 1". That is, plot the equilibrium values N \" as a function of 1', while indicating any sudden stability transitions