On a Coupled Time-Varying Beverton–Holt Model with Two Habitats Subject to Harvesting, Repopulation, and Mixed Migratory Flows of Populations

Abstract

Two time-varying Beverton–Holt models are investigated in which the population of the same species evolves jointly in two coupled habitats which can be subject to population exchanges. Both habitats can have different parameterizations concerning their intrinsic growth rates and their environment carrying capacities due to different environmental conditions. Mutual fluxes of populations in-between both habitats are possible together with harvesting actions. In one of the models harvesting acts on juvenile individuals. In the other proposed model, harvesting takes place on the adult populations after the reproduction cycle they have performed has ended. The second investigated model, contrarily to the first one, relies on an “a posteriori” harvesting action to the reproductive stage which is able to modify the stocks of population. The considered harvesting can also be negative to describe repopulation actions. The equilibrium points in steady-state and their stability properties as well as the extinction conditions and the boundedness, oscillation issues, and positivity of the solutions are also investigated.