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Artículo
Trajectory and global attractors for generalized processes
(American Institute of Mathematical Sciences, 2019-08)
In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem and, through this approach, some conditions for the existence of trajectory attractors are proved. ...
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
Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion
(Elsevier, 2022-08)
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay ...
Artículo
Global attractors for multivalued random semiflows generated by random differential inclusions with additive noise
(2001)
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
Asymptotic behavior of nonlocal partial differential equations with long time memory
(AIMS, 2022-10-01)
In this paper, it is first addressed the well-posedness of weak solutions to a nonlocal partial differential equation with long time memory, which is carried out by exploiting the nowadays well-known technique used by ...
Artículo
Determining asymptotic behavior from the dynamics on attracting sets
(Springer, 1999-04)
Two tracking properties for trajectories on attracting sets are studied. We prove that trajectories on the full phase space can be followed arbitrarily closely by skipping from one solution on the global attractor to ...
Artículo
About the Structure of Attractors for a Nonlocal Chafee-Infante Problem
(MDPI, 2021)
In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we ...
Artículo
Attractors for Parametric Delay Differential Equations and Their Continuous Behavior
(World Scientific, 2010)
The problem of the continuity of global attractors under minimal assumptions for a general class of parameterized delay differential equations is considered. The theory of equi-attraction developed by Li and Kloeden in ...
Artículo
Finite-dimensional global attractors in Banach spaces
(Elsevier, 2010-12-15)
We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls ...