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In this paper, Asada's five-dimensional nonlinear model describing the dynamic interaction of two regions connected through interregional trade and interregional capital movement with fixed exchange rates is applied to the conditions of Slovakia and the Czech Republic. The functions of consumptions, investments, interest rates, taxes, and net exports involved in the model are constructed based on quarterly data of these two countries from the period 2010-2017. The equilibrium was found and the conditions on the parameters were established, guaranteeing that the Jacobian matrix of the model has a pair of purely imaginary eigenvalues with the remaining three with negative real parts. The bifurcation equation of the model giving the information on the qualitative properties of its solutions around the equilibrium, including the existence of business cycles and their stability/instability, was obtained. Numerical simulations are presented showing that they are fully in compliance with the achieved theoretical results. [ABSTRACT FROM AUTHOR]