Mackey-Glass type delay differential equations near the boundary of absolute stability

For equations $x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta > 0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to zero when both $\zeta -1 >0$ and $h(\zeta-1)^{1/8}$ are less than some constant (independent on $h,\zeta$). This result gives additional insight to the conjecture about the equivalence between local and global asymptotical stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of Mathematical Analysis and Application

Yorke and Wright 3/2-stability theorems from a unified point of view

We consider a family of scalar delay differential equations $x'(t)=f(t,x_t)$, with a nonlinearity $f$ satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS, devoted to the fourth international conference on Dynamical Systems and Differential Equations, held at UNC at Wilmington, May 2002. Minor changes from the previous versio

GRAY BOX IDENTIFICATION WITH HOPFIELD NEURAL NETWORKS

In this work, a novel method, based upon Hopfield neural networks, is proposed for parameter estimation in the context of system identification. This subject is a very active field of research, because even when a model of a physical system is available, some parameters may be uncertain or tim

UNIVERSIDAD POLITÉCNICA DE MADRID

OF THE MASTER&apos;S THESIS........................................................................................ 2 RESUMEN DEL PROYECTO FIN DE CARRERA .......................................................................... 3 DIPLOMITYN TIIVISTELM ........................................................................................................ 7 FOREWORD.......................................................................................................................................... 8 TABLE OF CONTENTS....................................................................................................................... 9 ABBREVIATIONS AND SYMBOLS ................................................................................................ 11 1