Artículo
Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion
Autor/es | Langa Rosado, José Antonio
Robinson, James C. Rodríguez Bernal, Aníbal Suárez Fernández, Antonio |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2009 |
Fecha de depósito | 2016-05-16 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Identificador del proyecto | MTM2005-01412
FQM-02468 MTM2006–08262 920894 MTM2006-07932 FQM-520 |
Cita | Langa 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. |
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