  For a model system defined as combination of sequentially applied continuous
transformations of a sphere, the question of arrangement of the parameter space
around the domain of existence of the Plykin-type attractor is considered.
Results of numerical calculations are presented, including charts of dynamical
regimes and Lyapunov exponents on the parameter plane, as well as portraits of
attractors in characteristic regions of chaotic and regular dynamics. The
Plykin attractor region is determined and depicted using the computational
procedure for checking hyperbolicity, which consists in analyzing angles
between expanding and contracting tangent subspaces of typical trajectories on
the attractor. The Plykin attractor takes place in a bounded continuous region
of the parameter plane that corresponds to roughness (structural stability) of
the hyperbolic dynamics. Outside that region, various types of dynamics are
observed including non-hyperbolic chaos, periodic and quasiperiodic behaviors.
