  A non-autonomous flow system is introduced with an attractor of Plykin type
that may serve as a base for elaboration of real systems and devices
demonstrating the structurally stable chaotic dynamics. The starting point is a
map on a two-dimensional sphere, consisting of four stages of continuous
geometrically evident transformations. The computations indicate that in a
certain parameter range the map has a uniformly hyperbolic attractor. It may be
represented on a plane by means of a stereographic projection. Accounting
structural stability, a modification of the model is undertaken to obtain a set
of two non-autonomous differential equations of the first order with smooth
coefficients. As follows from computations, it has the Plykin type attractor in
the Poincar\'{e} cross-section.
