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.

Impact of Fear Behavior on Prey Population Growth Prey-Predator Interaction

“…The formulation of a mathematical model on prey will be developed in the form of a function with a fear effect based on the assumptions that have been given [23]. The function with the fear effect will be given on the growth of the prey species by multiplying the form 𝑓(𝛼, 𝛽, 𝑦), so that the form model (1) becomes…”

The Dynamics and Harvesting Effect Population One Prey Two Predator with Schooling Behavior

“…Harvesting business is carried out selectively on two populations of species. The fishing effort rate equation for prey and predator is 𝑞 𝐸 𝑥 and 𝑞 𝐸 𝑧, where and 𝑞 are the coefficients of the population of prey and predator species [20]. The mathematical model formed from these assumptions can be seen as follows:…”