1. In the species competition model (white tip shark vs. black tip shark):

{dW/dt = aW - bWB, dB/dt = cB - dWB}, where W(t) denotes the white tip shark population at time t, B(t) denotes the black tip shark population at time t, and a,b,c, and d are constants.

a. Develop a modified competition model of the white tip shark and black tip shark, assuming that in the case when white tip shark demonstrate exponential decay (so that a < 0 in the first equation) and that the black tip shark grows logistically with a population limit M.

b. Find the equilibrium point(s) of the modified model in part (a). Determine if the equilibrium point(s) are stable or unstable by analyzing graphically the motion in the vicinity of the equilibrium points in your model. Based on your analysis of this part, determine if coexistence is likely.