  The main aim of this paper is to detect dynamical properties of the
Gy\"orgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The
corresponding three-variable model given as a set of nonlinear ordinary
differential equations depends on one parameter, the flow rate. As certain
values of this parameter can give rise to chaos, the analysis was performed in
order to identify different dynamics regimes. Dynamical properties were
qualified and quantified using classical and also new techniques. Namely, phase
portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for
chaos, and approximate entropy. The correlation between approximate entropy and
the 0-1 test for chaos was observed and described in detail. Moreover, the
three-stage system of nested subintervals of flow rates, for which in every
level the 0-1 test for chaos and approximate entropy was computed, is showing
the same pattern. The study leads to an open problem whether the set of flow
rate parameters has Cantor like structure.
