Rodríguez Bernal, AníbalLanga, José A.Suárez Fernández , Antonio2023-06-202023-06-2020100022-039610.1016/j.jde.2010.04.001https://hdl.handle.net/20.500.14352/42014In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution for these models, which attracts any other complete bounded trajectory. Thus, we generalize the existence of a unique strictly positive stable (stationary) solution from the autonomous case and we extend to Lotka–Volterra systems the result for scalar logistic equations. To this end we present the sub-supertrajectory tool as a generalization of the now classical sub-supersolution method. In particular, we also conclude pullback and forwards permanence for the above models.engjournal articlehttp://www.sciencedirect.com/science/journal/00220396open access517.9Sub-supertrajectory methodLotka–Volterra competitionSymbiosis and prey–predator systemsAttracting complete trajectoriesEcuaciones diferenciales1202.07 Ecuaciones en Diferencias