Optimal mullets consumption by osprey population using utility function

. We consider the interaction between mullets and osprey populations. The main objective of this work is that the osprey must choose the predation intensity over time in a way that maximizes the present value of the utility stream derived by consuming mullets. The model has features of both convex and concave optimal control problems and therefore, phase plane analysis has to be combined with the problem of synthesis of bang-bang, singular and chattering solution pieces