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

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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 nondegenerate 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. © 2010 Elsevier Inc.

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Langa, J. A., Rodríguez-Bernal, A., & Suárez, 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. https://doi.org/10.1016/j.jde.2010.04.001

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