KONTROL OPTIMAL PREY DAN PREDATOR MODEL RANTAI MAKANAN ROSENZWEIG-MACARTHUR TIGA SPESIES

Abstract

The development of knowledge study about ecosistem grows fast in this last decade, one of the study is a model of food chain that include prey-predator. Rosenzweig-MacArthur’s food chain model  is one of the model that develop in the study about  prey and predator’s correlation  which at first include two species only. To approach the real situation, Rosenzweig-MacArthur added one new variable (super-predator) on super-predator model so that it became three species food chain model. Population density  function of prey-predator in the food chain model was influenced by time function and control profile to search optimal control function from model can be gained through the information that construct Rosenzweig-MagArthur food chain model. By optimal control principal, prey population and super-predator will be controlled through the prey carrying capacity (k) and death rate (mortality) of super-predator (d₃) to minimize variation agreed for the model of Rosenzweig-MacArthur three species. It was expected that from optimal control function which has been obtained, the three species will not extinct