Langa Rosado, José AntonioRobinson, James C.Rodríguez Bernal, AníbalSuárez Fernández, Antonio2016-05-162016-05-162009Langa Rosado, J.A., Robinson, J.C., Rodríguez Bernal, A. y Suárez Fernández, A. (2009). Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion.0036-14101095-7154http://hdl.handle.net/11441/41226Lotka-Volterra systems are the canonical ecological models used to analyze population dynamics of competition, symbiosis or prey-predator behaviour involving different interacting species in a fixed habitat. Much of the work on these models has been within the framework of infinite-dimensional dynamical systems, but this has frequently been extended to allow explicit time dependence, generally in a periodic, quasiperiodic or almost periodic fashion. The presence of more general non-autonomous terms in the equations leads to non-trivial difficulties which have stalled the development of the theory in this direction. However, the theory of non-autonomous dynamical systems has received much attention in the last decade, and this has opened new possibilities in the analysis of classical models with general non-autonomous terms. In this paper we use the recent theory of attractors for non-autonomous PDEs to obtain new results on the permanence and the existence of forwards and pullback asymptotically stable global solutions associated to non-autonomous Lotka-Volterra systems describing competition, symbiosis or prey-predator phenomena. We note in particular that our results are valid for prey-predator models, which are not order-preserving: even in the ‘simple’ autonomous case the uniqueness and global attractivity of the positive equilibrium (which follows from the more general results here) is new.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Lotka-Volterra competitionsymbiosis and prey-predator systemsnon-autonomous dynamical systemspermanenceattracting complete trajectoriesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1137/080721790