  We consider an autonomous system of partial differential equations for
one-dimensional distributed medium with periodic boundary conditions. Dynamics
in time consists of alternating birth and death of patterns with spatial phases
transformed from one stage of activity to another by the doubly expanding
circle map. So, attractor in the Poincar\'e section is uniformly hyperbolic, a
kind of Smale-Williams solenoid. Finite-dimensional models are derived as
ordinary differential equations for amplitudes of spatial Fourier modes (the 5D
and 7D models). Correspondence of the reduced models to the original system is
demonstrated numerically. Computational verification of the hyperbolicity
criterion is performed for the reduced models: the distribution of angles of
intersection for stable and unstable manifolds on the attractor is separated
from zero, i.e. the touches are excluded. The considered example gives a
partial justification to the old hopes that chaotic behavior of autonomous
distributed systems may be associated with uniformly hyperbolic attractors.
