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Article
Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs
(World Scientific Publishing, 2005-08)
In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the non-autonomous equation ut − ∆u = λu − b(t)u 2 with b(t) ∈ [b0, B0], 0 < b0 < B0 < 2b0. In particular, we prove the ...
Article
The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model
(Sociedad Española de Matemática Aplicada, 2010)
In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. In particular, under some conditions on the parameters, we prove the existence of a unique ...
Article
On the long time behavior of non-autonomous Lotka–Volterra models with diffusion via the sub-supertrajectory method
(Elsevier, 2010-07-15)
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. ...
Article
Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion
(Society for Industrial and Applied Mathematics, 2009)
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 ...
Article
Biodiversity and vulnerability in a 3D mutualistic system
(American Institute of Mathematical Sciences, 2014-10)
In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. We compare the dynamical properties of this system with the associated ...
Article
Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system
(Elsevier, 2007-05-15)
In this paper we determine the exact structure of the pullback attractors in non-autonomous problems that are perturbations of autonomous gradient systems with attractors that are the union of the unstable manifolds of a ...
Article
Pullback permanence in a non-autonomous competitive Lotka-Volterra model
(Elsevier, 2003-05-01)
The goal of this work is to study in some detail the asymptotic behaviour of a non-autonomous Lotka-Volterra model, both in the conventional sense (as t → ∞) and in the “pullback” sense (starting a fixed initial condition ...
Article
Bifurcations in non-autonomous scalar equations
(Elsevier, 2006-02)
In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, and applied these to investigate the bifurcations in some simple models. In this paper we ...
Article
Existence and nonexistence of unbounded forward attractor for a class of non-autonomous reaction diffusion equations
(American Institute of Mathematical Sciences, 2007)
The goal of this work is to study the forward dynamics of positive solutions for the nonautonomous logistic equation ut − ∆u = λu − b(t)up, with p > 1, b(t) > 0, for all t ∈ R, limt→∞ b(t) = 0. While the pullback asymptotic ...
Article
Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system
(IOPscience, 2003-07)
Lotka-Volterra systems have been extensively studied by many authors, both in the autonomous and non-autonomous cases. In previous papers the time asymptotic behaviour as t → ∞ has been considered. In this paper we also ...