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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
Capturing the non-stationarity of whole-brain dynamics underlying human brain states
(Elsevier, 2021-09-08)
Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central unsolved problem in neuroscience. We approximate the non-stationary landscape sustained by the human ...
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
Informational structures and informational fields as a prototype for the description of postulates of the integrated information theory
(MDPI, 2019-05)
Informational Structures (IS) and Informational Fields (IF) have been recently introduced to deal with a continuous dynamical systems-based approach to Integrated Information Theory (IIT). IS and IF contain all the ...
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
Extremal bounded complete trajectories for nonautonomous reaction-diffusion equations with discontinuous forcing term
(Springer, 2020)
In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term of Heaviside type. Using this principle, we study the structure of the global attractor in both the ...
Artículo
Tracking Properties of Trajectories On Random Attracting Sets
(1999)
The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic differential equations. In this paper some results on the relation between the dynamics on random ...
Artículo
What lies underneath: Precise classification of brain states using time-dependent topological structure of dynamics
(PLOS, 2022)
The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between interconnected brain regions. Until now, most efforts of capturing the causal mechanistic generating ...
Artículo
Morse decomposition of global attractors with infinite components
(2015)
In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, we are able to prove that the gradient dynamics on Morse sets together with a separation assumption ...
Artículo
Continuity of Lyapunov Functions and of Energy Level for a Generalized Gradient Semigroup
(2012)
The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (di erentiable along solutions)-de ned on the whole phase space- which proves ...