Global stability of a Lotka-Volterra piecewise-smooth system with harvesting actions and two predators competing for one prey

The global dynamics of a three-dimensional Lotka-Volterra system described by two predator species competing for one prey and with human harvesting action on the predator species is studied in this paper. The harvesting action is introduced by means of two switching control actions defined on the predator species. A wellknown result in the study of ecosystem modeling is that there are two states of coexistence of one of the predatory species with the prey species assuming that the principle of competitive exclusion or coexistence of competing species is fulfilled. In this sense, the three species cannot coexist in this class of system. In this work, it is proved that there is a global stable equilibrium point where the three species can coexist due to the proposed harvesting action. (c) 2023 Elsevier Inc. All rights reserved.