Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion
Lotka-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 dynam...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41226 |
| Acesso em linha: | http://hdl.handle.net/11441/41226 https://doi.org/10.1137/080721790 |
| Access Level: | acceso abierto |
| Palavra-chave: | Lotka-Volterra competition symbiosis and prey-predator systems non-autonomous dynamical systems permanence attracting complete trajectories |
| Resumo: | Lotka-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. |
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