STABILITY ANALYSIS AND OPTIMAL CONTROL ON THE MODEL HARVESTING OF PREY PREDATOR WITH FUNGSIONAL RESPONSE TYPE III

Ecosystem is the reciprocal relations between living things and their environment. Relationships between organisms or individuals will not be separated from the process of eating and being eaten. On ecological science event called the food chain. In the food chain, there is the term prey and predator, where both are interdependent of each other. The behavior or characteristics of the predator-prey can be modeled mathematically and historically has been developed by researchers. Predator-prey system basic model in general, first introduced by Lotka-Voltera, later developed by Leslie and continued by Holling-Tanner. On the model of Holling-Tanner developed a response function on the function called predator Holling. In this research, the stabilty analysis and optimal harvesting control are done on predator prey system with Holling response functions III. Considering the ecosystem, especially in the sea there is a bite to eat, interaction so that the appropriate harvest strategies are needed for maximum commercial benefit while maintaining the sustainability of the species. In this case, the optimum harvesting amount obtained using the Principle of Maximum Pontyagin. Keywords : Model of Prey predator, Function response Holling type III, Harvesting, The principle of Pontryagin’s maximum