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Artículo
Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
(American Institute of Mathematical Sciences (AIMS), 2020-08)
In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems ...
Artículo
Invariant measures for the 3D globally modified Navier-Stokes equations with unbounded variable delays
(Elsevier, 2020-12)
This article investigates the three-dimensional globally modified Navier-Stokes equations with unbounded variable delays. Firstly, we prove the global well-posedness of the solutions, and give the existence of the pullback ...
Artículo
Trajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applications
(Elsevier, 2020-06)
In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the existence of trajectory statistical solutions for autonomous evolution equations. Then we establish that ...
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 ...