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On the long time behavior of non-autonomous Lotka–Volterra models with diffusion via the sub-supertrajectory method

 

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Opened Access On the long time behavior of non-autonomous Lotka–Volterra models with diffusion via the sub-supertrajectory method
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Author: Langa Rosado, José Antonio
Rodríguez Bernal, Aníbal
Suárez Fernández, Antonio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2010-07-15
Published in: Journal of Differential Equations, 249 (2), 414-445.
Document type: Article
Abstract: 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.
Cite: 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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URI: http://hdl.handle.net/11441/43245

DOI: 10.1016/j.jde.2010.04.001

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