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Artículo
Flattening, squeezing and the existence of random attractors
(Royal Society, 2007-01)
The study of qualitative properties of random and stochastic differential equations is now one of the most active fields in the modern theory of dynamical systems. In the deterministic case, the properties of flattening ...
Artículo
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 ...
Artículo
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 ...
Artículo
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 ...
Artículo
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 ...
Artículo
Pullback attractors of nonautonomous and stochastic multivalued dynamical systems
(2003)
In this paper we study the existence of pullback global attractors for multivalued processes generated by differential inclusions. First, we define multivalued dynamical processes, prove abstract results on the existence ...
Artículo
The stability of attractors for non-autonomous perturbations of gradient-like systems
(Elsevier, 2007-03-15)
We study the stability of attractors under non-autonomous perturbations that are uniformly small in time. While in general the pullback attractors for the nonautonomous problems converge towards the autonomous attractor ...
Artículo
Global Attractors for Multivalued Random Dynamical Systems
(2002)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the cocycle property. We show how this is a suitable framework for the study of the asymptotic behaviour ...
Artículo
Stabilisation of differential inclusions and PDEs without uniqueness by noise
(2008)
We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without uniqueness of solutions can be stabilised by adding some suitable Itˆo noise as an external perturbation. ...