The paper is concerned with the improvement of sufficient conditions for the exponential stability of Hopfield-type neural networks displaying interaction delays. The results are based on a method obtained in our previous work that combines an idea suggested by Malkin for studying the absolute stability of a nonlinear system via their linearisations and a procedure proposed by Kharitonov for co...

We consider the problem " 2 u ? u + f (u) = 0 in u > 0 in ; @u @ = 0 on @; where is a bounded smooth domain in R N , " > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as " approaches zero, at a critical point of the mean curvature function H(P); P 2 @. It is also known ...

Artificial neural networks for solving different variants of linear programming problems are proposed and analyzed through Liapunov direct method. An energy function with an exact penalty term is associated to each variant and leads to a discontinuous dynamic gradient system model of an artificial neural network. The objective is to derive conditions that the network gains must satisfy in order...

In this paper, we study the stabilization of nonlinear systems in critical cases by using the center manifold reduction technique. Three degenerate cases are considered, wherein the linearized model of the system has two zero eigenvalues, one zero eigenvalue and a pair of nonzero pure imaginary eigenvalues, or two distinct pairs of nonzero pure imaginary eigenvalues; while the remaining eigenva...

In a study of articles published in the Proceedings of the National Academy of Sciences, Gunther Eysenbach discovered a significant citation advantage for those articles made freely-available upon publication (Eysenbach 2006). While the author attempted to control for confounding factors that may have explained the citation differential, the study was unable to control for characteristics of th...