Recall that in this model, the parameter v > 0 denotes the value of the resource to be divided between the players, and c > 0 represents the cost of fighting over that resource. (a) (1 mark) Let x(t) denote the frequency of hawks in the population at time t. Set up the replicator equation to describe the change in frequency of the hawks over time, dx dt . (b) (1 mark) Find all equilibria of the replicator equation. (c) (3 marks) Construct a bifurcation diagram that describes the replicator dynamics as the cost of fighting varies (that is, create a bifurcation diagram for c (0, )). Note that you can treat the value of the resource, v, as fixed. Remember to clearly indicate the direction of selection and the stability of all equilibria