Rosenzweig-MacArthur model considering the function that protects a fixed amount of prey for population dynamics

Abstract

Populations can grow, disappear or remain in time and this depends on their birth rates, mortality, immigration and emigration. For a long time, species have disappeared and others are at the same risk if protective policies are not implemented to guarantee their survival. It is necessary to consider mathematical models that help conserve the environment. The analysis of the Rosenzweig-MacArthur model was performed considering the function that protects a fixed amount of prey. For the analytical study, the qualitative theory of the systems of differential equations is used. Considering the use of shelters by dams with the functions proposed by Maynard-Smith. It is shown that the refuge influences the stability of the only equilibrium point inside the first quadrant and produces important effects in the dynamics of the prey-prey model.

Density Dependent Delayed Migration for Rosenzweig-Macaurther Model with Holling Type II Predator Functional Response

“…The model assumed that in the absence of the predator species, the prey will grow unboundedly. The Rosenzweig-Macarthur model improved the Lotka-Volterra model by including a carrying capacity for the prey species to account for the fact that the prey will grow governed by the available sustaining resources in the absence of the predation in a homogeneous environment [4,5,6,7,8,9]. A homogeneous environment is considered in the classical predator-prey system, but in real life, the environment is heterogeneous and its connected by migration [1,2,10].…”