  The recent precise photometric observations and successes of the modelling
efforts transformed our picture of the pulsation of RR Lyrae stars. The
discovery of additional frequencies and the period doubling phenomenon revealed
that a significant interaction may occur between pulsational modes. The signs
of irregularities were detected both in observed light curves and hydrodynamic
calculations.
  In this paper we present the analysis of four peculiar hydrodynamic model
solutions. All four solutions were found to be chaotic. The fractal (Lyapunov)
dimensions of their attractors were calculated to be ~2.2. We also investigated
possible resonances between the fundamental mode and the first overtone in the
dynamical neighbourhood of these models. The most important is the 6:8
resonance that was also detected in the Kepler observations of RR Lyrae itself.
These results reveal that the investigation of chaotic models is important in
discovering and understanding resonances in RR Lyrae stars.
