RT info:eu-repo/semantics/article
T1 Existence of global attractor for a nonautonomous state-dependent delay differential equation of neuronal type
A1 Elia, Cinzia
A1 Maroto Camarena, Ismael
A1 Núñez Jiménez, María del Carmen
A1 Obaya, Rafael
AB The analysis of the long-term behavior of the mathematical model of a neuralnetwork constitutes a suitable framework to develop new tools for the dynamicaldescription of nonautonomous state-dependent delay equations (SDDEs).The concept of globalattractor is given, and some results which establish properties ensuringits existence and providing a description of its shape, are proved.Conditions for the exponential stability of the global attractorare also studied. Some propertiesof comparison of solutions constitute a key inthe proof of the main results, introducing methods of monotonicityin the dynamical analysis of nonautonomous SDDEs.Numerical simulations of some illustrative models showthe applicability of the theory.
SN 1007-5704
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40500
UL http://uvadoc.uva.es/handle/10324/40500
LA spa
NO Communications in Nonlinear Science and Numerical Simulation 78 (November) (2019), 104874, 1-23
DS UVaDOC
RD 30-abr-2024