  One of the main tasks in the study of financial and economic processes is
forecasting and analysis of the dynamics of these processes. Within this task
lie important research questions including how to determine the qualitative
properties of the dynamics and how best to estimate quantitative indicators.
  These questions can be studied both empirically and theoretically. In the
empirical approach, one considers the real data represented by time series,
identifies patterns of their dynamics, and then forecasts short- and long-term
behavior of the process. The second approach is based on postulating the laws
of dynamics for the process, deriving mathematical dynamic models based on
these laws, and conducting subsequent analytical investigation of the dynamics
generated by the models.
  To implement these approaches, both numerical and analytical methods can be
used. It should be noted that while numerical methods make it possible to study
complex models, the possibility of obtaining reliable results using them is
significantly limited due to calculations being performed only over finite-time
intervals, numerical errors, and the unbounded space of initial data sets. In
turn, analytical methods allow researchers to overcome these problems and to
obtain exact qualitative and quantitative characteristics of the process
dynamics. However, their effective applications are often limited to
low-dimensional models. In this paper, we develop analytical methods for the
study of deterministic dynamic systems. These methods make it possible not only
to obtain analytical stability criteria and to estimate limiting behavior, but
also to overcome the difficulties related to implementing reliable numerical
analysis of quantitative indicators. We demonstrate the effectiveness of the
proposed methods using the mid-size firm model suggested recently by V.I.
Shapovalov.
