  Cyclicity and instability inherent in the economy can manifest themselves in
irregular fluctuations, including chaotic ones, which significantly reduces the
accuracy of forecasting the dynamics of the economic system in the long run. We
focus on an approach, associated with the identification of a deterministic
endogenous mechanism of irregular fluctuations in the economy. Using of a
mid-size firm model as an example, we demonstrate the use of effective
analytical and numerical procedures for calculating the quantitative
characteristics of its irregular limiting dynamics based on Lyapunov exponents,
such as dimension and entropy. We use an analytical approach for localization
of a global attractor and study limiting dynamics of the model. We estimate the
Lyapunov exponents and get the exact formula for the Lyapunov dimension of the
global attractor of this model analytically. With the help of delayed feedback
control (DFC), the possibility of transition from irregular limiting dynamics
to regular periodic dynamics is shown to solve the problem of reliable
forecasting. At the same time, we demonstrate the complexity and ambiguity of
applying numerical procedures to calculate the Lyapunov dimension along
different trajectories of the global attractor, including unstable periodic
orbits (UPOs).
