Optimal harvesting and stability of predator-prey model with holling type II predation respon function and stage-structure for predator

Abstract

This article develops mathematical models with structural stages from predators, immature and mature predators. The predation function of mature predators follows the Holling II response function. We assume that the immature predator population has the economic value, therefor the harvesting function is included in this model. In this model an analysis of the equilibrium point and stability of the interior equilibrium point is carried out. Analysis of the stability of the interior equilibrium points is done by linearization method and pay attention to the eigenvalues of the characteristics of the Jacobi matrix obtained. Analysis of equilibrium point stability is carried out before and after harvesting. The result is obtained by each of the three equilibrium points. At the equilibrium point of the interior with stable harvesting a local maximum profit analysis is obtained from the exploitation business. Based on the results of the analysis, it is obtained the value of harvesting business which provides a stable equilibrium point and maximum profit.