Artículo
On the long time behavior of non-autonomous Lotka–Volterra models with diffusion via the sub-supertrajectory method
Autor/es | Langa Rosado, José Antonio
Rodríguez Bernal, Aníbal Suárez Fernández, Antonio |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2010-07-15 |
Fecha de depósito | 2016-07-06 |
Publicado en |
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Resumen | In 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 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. |
Identificador del proyecto | MTM2008-0088
HF2008-0039 PHB2006-003PC MTM2006-08262 CCG07-UCM/ESP-2393 |
Cita | Langa Rosado, J.A., Rodríguez Bernal, A. y Suárez Fernández, A. (2010). On the long time behavior of non-autonomous Lotka–Volterra models with diffusion via the sub-supertrajectory method. Journal of Differential Equations, 249 (2), 414-445. |
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