Model Matematika Rantai Makanan Tiga Spesies

Abstract

Abstract –– Predation interaction between two species have been described in Lotka-Volterra mathematical model. But in an ecosystem, predation interaction involving more than two species. In this study will be discussed predation interaction involving three species in a food chain. Obtained mathematical model will be analyzed by finding the stability of fixed point, the stability of fixed point will be analyzed with Routh-Hurwitz criterion. The model consists of three differential equations representing each species. The model has four fixed points, the fourth fixed point is stable, the first fixed point is not stable but the third and second fixed point are stable with certain conditions. The result of analisys show that three populations does not become extinct if product of species I growth rate with spesies III growth rate is greater than product of species I death rate with species III death rate.

Keywords –– Food Chain, Fixed Point, Routh-Hurwitz