ON THE COMBINED HARVESTING OF A PREY-PREDATOR SYSTEM

Abstract

The authors consider the combined harvesting of a prey-predator system in which both the prey and the predator species obey the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of both the exploited and unexploited systems is examined. The possibility of existence of bionomic equilibria is discussed. The optimal harvest policy is studied and the solution is derived in the equilibrium case by using Pontryagin’s maximal principle. The biological as well as economic aspects of the optimal equilibrium solution are discussed. Finally, the model is recast into an S-system and its numerical solutions are derived in several cases using the ESSYNS algorithm.