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oai:docta.ucm.es:20.500.14352/497072023-08-28T02:25:02Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense author Rodríguez Bernal, Aníbal author Langa, José A. author Robinson, James C. author Suárez, Antonio 2023-06-20T09:29:27Z 2023-06-20T09:29:27Z 2009 0036-1410 10.1137/080721790 https://hdl.handle.net/20.500.14352/49707 http://epubs.siam.org/sima/resource/1/sjmaah Lotka–Volterra systems are the canonical ecological models used to analyze population dynamics of competition, symbiosis, or prey-predator behavior 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 nonautonomous terms in the equations leads to nontrivial difficulties which have stalled the development of the theory in this direction. However, the theory of nonautonomous dynamical systems has received much attention in the last decade, and this has opened new possibilities in the analysis of classical models with general nonautonomous terms. In this paper we use the recent theory of attractors for nonautonomous PDEs to obtain new results on the permanence and the existence of forwards and pullback asymptotically stable global solutions associated to nonautonomous 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. eng Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion journal article URL https://docta.ucm.es/bitstreams/cf134dde-b9c2-4457-8115-0a537e0213f1/download File MD5 a0adac8efceaa8fe5134e3019c238260 274652 application/pdf 2008permanence-09.pdf URL https://docta.ucm.es/bitstreams/14d6b362-ebe9-4b52-9683-eee32d8a6368/download File MD5 4bca123012525096b7244b3eb6523aa3 102253 text/plain 2008permanence-09.pdf.txt