The economic activity indicators in Poland during the years 1995‒2011 exhibit various cyclical patterns. Employing the Christiano – Fitzgerald band-pass filter and unobserved components model it is shown that the cyclical processes of Polish economic activity are driven by overlapping higher frequency fluctuations (3‒4 years) and longer cycles of 8.5 years. The cyclical fluctuations of construction, transportation and trade are dissimilar to gross value added. Economic activity in transportation leads and in construction lags the fluctuations of gross value added. Cyclical fluctuations of gross value added seem to be determined by industry and construction. Manufacturing, especially capital and intermediate goods fluctuations are responsible for the variation of industry. The production of non-durable consumer goods, energy and production of electric power are relatively the most desynchronized compared to industry. Production of electric power leads industrial production. Capital goods, intermediate goods and energy cycle phases are asymmetric – the slowdown lasts shorter and has higher amplitude compared to expansion. During the last crisis occurred the intensified variation of economic activity in Poland.

The dynamic development of science requires constant improvement of approaches to modeling physical processes and phenomena. Practically all scientific problems can be described by systems of differential equations. Many scientific problems are described by systems of differential equations of a special class, which belong to the group of so-called singularly perturbed differential equations. Mathematical models of processes described by such differential equations contain a small parameter near the highest derivatives, and it was the presence of this small factor that led to the creation of a large mathematical theory. The work proposes a developed algorithm for constructing uniform asymptotics of solutions to systems of singularly perturbed differential equations.