| Contents |
| We propose a class of the dynamical systems as nonlinear matrix
models for macro system dynamics in the presence of limiting
factor. The dynamical systems are generated by non-invertible
generally, map $F$ of the form $F y = \Phi(\|y\|) A y$ in some
compact $\mathrm{X} \subset \mathbb{R}^n$. Here $\mathrm{R}^n$ is
$n$- dimensional real vector-space, $A$ is a matrix of $n$ order,
$\|\cdot\|$ is a vector norm in $\mathrm{R}^n$ and $\Phi(\|y\|)$
is a (scalar) function playing a role of a limiting factor. The
results of qualitative theory we develop for this class of the
dynamical systems are essentially used in modelling. In this talk
we present an application package for Matlab which we elaborate
for the numerical realization of models. A computer method is
developed for determining the macro system asymptotic behavior. We
call it the method of one-dimensional superpositions. The
advantages of applying the results of the qualitative research and
using the method of one-dimensional superpositions in computer
simulation of the dynamics of macro systems governed by this class
of models are discussed. In particular, the method proved to be
very useful for a large number of macro system's components ($n$)
and big periods ($> n$ and $> n^2$) of asymptotically stabilized
macro system structure if to denote the macro system structure (at
the time $m$) by the vector $\|F^m y\|^{-1}F^m y$. |
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