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The main aim of this paper is to detect embedded dynamics of the Györgyi-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, an 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, approximate entropy, and the maximal Lyapunov exponent. The correlation between approximate entropy and the 0–1 test for chaos was observed and described in detail. The main discovery was that the three-stage system of nested sub-intervals of flow rates showed the same pattern in the 0–1 test for chaos and approximate entropy at every level. The investigation leads to the open problem of whether the set of flow rate parameters has Cantor-like structure.

The main aim of this paper is to analyze the dynamical properties of a model with a closed curve equilibrium. The corresponding three-variable model is given as a set of nonlinear ordinary differential equations containing non-smooth functions. The dynamics of the model are studied depending on three parameters. For this purpose, new methods, as the 0-1 test for chaos and approximate entropy, are applied. Using these tools, the dynamics are quantified and qualified. It is shown that depending on the system’s parameters, the system exhibits both irregular (chaotic) and regular (periodic) character.