709 research outputs found
Existence of global attractor for a nonautonomous state-dependent delay differential equation of neuronal type
The analysis of the long-term behavior of the mathematical model of a neural
network constitutes a suitable framework to develop new tools for the dynamical
description of nonautonomous state-dependent delay equations (SDDEs).
The concept of global
attractor is given, and some results which establish properties ensuring
its existence and providing a description of its shape, are proved.
Conditions for the exponential stability of the global attractor
are also studied. Some properties
of comparison of solutions constitute a key in
the proof of the main results, introducing methods of monotonicity
in the dynamical analysis of nonautonomous SDDEs.
Numerical simulations of some illustrative models show
the applicability of the theory.Ministerio de Economía y Competitividad / FEDER, MTM2015-66330-PMinisterio de Ciencia, Innovación y Universidades, RTI2018-096523-B-I00European Commission, H2020-MSCA-ITN-201
Asymptotic behavior of solutions of nonautonomous neutral dynamical systems
Producción CientíficaThis paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the trajectories of problems described by this kind of equations, such us compartmental systems and neural networks among many others. Precisely, more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non-neutral part.MICIIN/FEDER Grant RTI2018-096523-B-100H2020-MSCA-ITN-2014 643073 CRITICS
Lyapunov functions for linear nonautonomous dynamical equations on time scales
The existence of a Lyapunov function is established following a method of Yoshizawa for the uniform exponential asymptotic stability of the zero solution of a nonautonomous linear dynamical equation on a time scale with uniformly bounded graininess
On the instability of linear nonautonomous delay systems
summary:The unstable properties of the linear nonautonomous delay system , with nonconstant delay , are studied. It is assumed that the linear system is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function and the results depending on the asymptotic properties of the delay function
- …