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For a model system defined as combination of sequentially applied continuoustransformations of a sphere, the question of arrangement of the parameter spacearound the domain of existence of the Plykin-type attractor is considered.Results of numerical calculations are presented, including charts of dynamicalregimes and Lyapunov exponents on the parameter plane, as well as portraits ofattractors in characteristic regions of chaotic and regular dynamics. ThePlykin attractor region is determined and depicted using the computationalprocedure for checking hyperbolicity, which consists in analyzing anglesbetween expanding and contracting tangent subspaces of typical trajectories onthe attractor. The Plykin attractor takes place in a bounded continuous regionof the parameter plane that corresponds to roughness (structural stability) ofthe hyperbolic dynamics. Outside that region, various types of dynamics areobserved including non-hyperbolic chaos, periodic and quasiperiodic behaviors.

Parameter space arrangement of a model system nearby domain of existence of Plykin type attractor