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

Rodríguez Bernal, Aníbal and Langa, José A. and Suárez Fernández , Antonio (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). pp. 414-445. ISSN 0022-0396

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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.


Item Type:Article
Uncontrolled Keywords:Sub-supertrajectory method; Lotka–Volterra competition; Symbiosis and prey–predator systems; Attracting complete trajectories
Subjects:Sciences > Mathematics > Differential equations
ID Code:13978
Deposited On:30 Nov 2011 09:20
Last Modified:06 Feb 2014 09:57

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