Abstract: The problems of globally exponential stability and dissipativity analysis for static neural networks (NNs) with time delay is investigated in this paper. Some delay-dependent stability criteria are established for static NNs with time delay using the delay partitioning technique. In terms of this criteria, the delay-dependent sufficient condition is given to guarantee the dissipativity of static NNs with time delay. All the given results in this paper are not only dependent upon the time delay but also upon the number of delay partitions. Two numerical examples are used to show the effectiveness of the proposed methods.
Abstract: This article is dedicated to development of
mathematical models for determining the dynamics of
concentration of hazardous substances in urban turbulent
atmosphere. Development of the mathematical models implied
taking into account the time-space variability of the fields of
meteorological items and such turbulent atmosphere data as vortex
nature, nonlinear nature, dissipativity and diffusivity. Knowing the
turbulent airflow velocity is not assumed when developing the
model. However, a simplified model implies that the turbulent and
molecular diffusion ratio is a piecewise constant function that
changes depending on vertical distance from the earth surface.
Thereby an important assumption of vertical stratification of urban
air due to atmospheric accumulation of hazardous substances
emitted by motor vehicles is introduced into the mathematical
model. The suggested simplified non-linear mathematical model of
determining the sought exhaust concentration at a priori unknown
turbulent flow velocity through non-degenerate transformation is
reduced to the model which is subsequently solved analytically.