6,519 research outputs found
Global exponential stability of nonautonomous neural network models with unbounded delays
For a nonautonomous class of n-dimensional di erential system with in nite delays, we give
su cient conditions for its global exponential stability, without showing the existence of an
equilibrium point, or a periodic solution, or an almost periodic solution. We apply our main
result to several concrete neural network models, studied in the literature, and a comparison of
results is given. Contrary to usual in the literature about neural networks, the assumption of
bounded coe cients is not need to obtain the global exponential stability. Finally, we present
numerical examples to illustrate the e ectiveness of our results.The paper was supported by the Research Center of Mathematics of University of Minho with the Portuguese Funds from the FCT - “Fundação para a Ciência e a Tecnologia”, through the Project UID/MAT/00013/2013. The author thanks the referees for valuable comments.info:eu-repo/semantics/publishedVersio
Global stability of a Cohen-Grossberg neural network with both time-varying and continuous distributed delays
In this paper, a generalized neural network of Cohen-Grossberg type with both discrete
time-varying and distributed unbounded delays is considered. Based on M-matrix theory, sufficient conditions are established to ensure the existence and global attractivity of an equilibrium point. The global exponential stability of the equilibrium is also addressed,
but for the model with bounded discrete time-varying delays. A comparison of results
shows that these results generalize and improve some earlier publications.Fundação para a Ciência e a Tecnologia (FCT)Universidade do Minho. Centro de Matemática (CMAT
Broad Histogram Method for Continuous Systems: the XY-Model
We propose a way of implementing the Broad Histogram Monte Carlo method to
systems with continuous degrees of freedom, and we apply these ideas to
investigate the three-dimensional XY-model with periodic boundary conditions.
We have found an excellent agreement between our method and traditional
Metropolis results for the energy, the magnetization, the specific heat and the
magnetic susceptibility on a very large temperature range. For the calculation
of these quantities in the temperature range 0.7<T<4.7 our method took less CPU
time than the Metropolis simulations for 16 temperature points in that
temperature range. Furthermore, it calculates the whole temperature range
1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte
Carlo method for the range 2.1<T<2.2. Our way of treatment is general, it can
also be applied to other systems with continuous degrees of freedom.Comment: 23 pages, 10 Postscript figures, to be published in Int. J. Mod.
Phys.
A universal approach for drainage basins
Drainage basins are essential to Geohydrology and Biodiversity. Defining
those regions in a simple, robust and efficient way is a constant challenge in
Earth Science. Here, we introduce a model to delineate multiple drainage basins
through an extension of the Invasion Percolation-Based Algorithm (IPBA). In
order to prove the potential of our approach, we apply it to real and
artificial datasets. We observe that the perimeter and area distributions of
basins and anti-basins display long tails extending over several orders of
magnitude and following approximately power-law behaviors. Moreover, the
exponents of these power laws depend on spatial correlations and are invariant
under the landscape orientation, not only for terrestrial, but lunar and
martian landscapes. The terrestrial and martian results are statistically
identical, which suggests that a hypothetical martian river would present
similarity to the terrestrial rivers. Finally, we propose a theoretical value
for the Hack's exponent based on the fractal dimension of watersheds,
. We measure for Earth, which is close to
our estimation of . Our study suggests that Hack's law can
have its origin purely in the maximum and minimum lines of the landscapes.Comment: 20 pages, 6 Figures, and 1 Tabl
Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays
For a general Cohen-Grossberg neural network model with potentially unbounded time-varying
coeffi cients and infi nite distributed delays, we give su fficient conditions for its global asymptotic
stability. The model studied is general enough to include, as subclass, the most of famous
neural network models such as Cohen-Grossberg, Hopfi eld, and bidirectional associative memory.
Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As
illustrated, the results are applied to several concrete models studied in the literature and a
comparison of results shows that our results give new global stability criteria for several neural
network models and improve some earlier publications.The second author research was suported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the project PEstOE/MAT/UI0013/2014. The authors thank the referee for valuable comments
Boundedness and global exponential stability for delayed differential equations with applications
The boundedness of solutions for a class of n-dimensional differential equations with distributed delays is established by assuming the existence of instantaneous negative feedbacks which dominate the delay effect. As an important by-product, some criteria for global exponential stability of equilibria are obtained. The results are illustrated with applications to delayed neural networks and population dynamics models.POCI 2010CMATFundação para a Ciência e a Tecnologia (FCT) - SFRH/BD/29563/2006CMAFFEDE
General criteria for asymptotic and exponential stabilities of neural network models with unbounded delays
For a family of differential equations with infinite delay, we give sufficient conditions for the global asymptotic, and global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Cohen-Grossberg type, with both bounded and unbounded distributed delay, for which general asymptotic and exponential stability criteria
are derived. As illustrations, the results are applied to several concrete models studied in the literature, and a comparison of results is given.Fundação para a Ciência e a Tecnologia (FCT) - 2009-ISFL-1-209Universidade do Minho. Centro de Matemática (CMAT
A note on stability of impulsive scalar delay differential equations
For a class of scalar delay differential equations with impulses and satisfying a Yorke-type
condition, criteria for the global asymptotic stability of the zero solution are established. These
equations possess a non-delayed feedback term, which will be used to refine the general results on
stability presented in recent literature. The usual requirements on the impulses are also relaxed.
As an application, sufficient conditions for the global attractivity of a periodic solution for an
impulsive periodic model are given.This research was supported by Fundacao para a Ciencia e a Tecnologia (Portugal), under the Projects UID/MAT/04561/2013 (T. Faria) and UID/MAT/00013/2013 (J. J. Oliveira)
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