Search
Now showing items 1-9 of 9
Article
Finite-Dimensionality of Tempered Random Uniform Attractors
(Springer New York, 2021)
Finite-dimensional attractors play an important role in finite-dimensional reduction of PDEs in mathematical modelization and numerical simulations. For non-autonomous random dynamical systems, Cui and Langa (J Differ ...
Article
Continuity and topological structural stability for nonautonomous random attractors
(World scientific, 2021-09-29)
In this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. ...
PhD Thesis
Finite-dimensionality of attractors for dynamicl systems wigh applications: deterministic and random settings
(2021-01-27)
In this work we obtain estimates on the fractal dimension of attractors in three different settings: global attractors associated to autonomous dynamical systems, uniform attractors associated to non-autonomous dynamical ...
Article
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 ...
Article
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 ...
Article
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 ...
PhD Thesis
Robustness of nonuniform and random exponential dichotomies with applications to differential equations
(2022-03-17)
In this thesis, we study hyperbolicity for deterministic and random nonautonomous dynamical systems and their applications to differential equations. More precisely, we present results in the following topics: nonuniform ...
Article
The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations
(ScienceDirect, 2021-01-01)
In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies ...
PhD Thesis
Characterization of attractors for non-autonomous dynamical systems: Applications to non-dissipative case and ecological models
(2024-02-23)
Esta tesis está dedicada a la exploración de atractores para sistema dinámicos. Nuestro análisis sigue dos enfoques distintos: uno más abstracto, centrándose en atractores no acotados, y otra investigación más aplicada ...