The stability analysis of neural networks is important in the applications and has been studied by many authors. However, only recently has the stability of stochastic models of neural networks been investigated. In this paper we analyse the global asymptotic stability of a class of neural networks described by a stochastic delay di®erential equation. It can be argued that such a model is as co...

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...

In this article we consider derive a macroscopic model for root length density evolution, starting from a discrete mesh of roots, using homogenization. In the microscopic model each roots grows vertically according to an ordinary di erential equation. The roots growth rates depend on the spatial repartition of nutrient in the soil, which also evolves in time, leading to a fully coupled nonlinea...

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

A new algorithm of determination of coe cients of multidimensional heat equations on the basis of temperature measurements is proposed. A system of stochastic di erential equations (SDE) can be assigned to a linear multidimensional heat equation. The solution of the heat equation can be obtained by solving the corresponding SDE by the method of statistical modeling. The sensitivity analysis is ...

The suitability of methods from multidimensional systems theory and digital signal processing for the e cient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial di erential equation into a transfer function description of a multidimensional continuous system. It serves as the...

Under appropriate assumptions, it is shown that there is a di eomorphism that transforms solutions of the implicit di erential equation

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

We study a singular di$usion on Euclidean space which is characterized by the solution of a classical Itô stochastic di$erential equation in which the di$usion coe2cient is not necessarily of full rank. Our motivation is in earlier results of Basak (J. Multivariate Anal. 39 (1991) 44) and Basak and Bhattacharya (Ann. Probab. 20 (1992) 312), who establish su2cient conditions for singular di$usio...

generalized solution on neumann problem of the fourth order ordinary dierential equation in space w2 (0; b) has been discussed , we obtain the condition on b.v.p when the solution is in classical form. formulation of quintic spline function has been derived and the consistency relations are given.numerical method,based on quintic spline approximation has been developed. spline solution of the...