  We consider an autonomous system constructed as modification of the logistic
differential equation with delay that generates successive trains of
oscillations with phases evolving according to chaotic maps. The system
contains two feedback loops characterized by two generally distinct retarding
time parameters. In the case of their equality, chaotic dynamics is associated
with the Smale-Williams attractor that corresponds to the double-expanding
circle map for the phases of the carrier of the oscillatory trains.
Alternatively, at appropriately chosen two different delays attractor is close
to torus with Anosov dynamics on it as the phases are governed by the Fibonacci
map. In both cases the attractors manifest robustness (absence of regularity
windows under variation of parameters) and presumably relate to the class of
structurally stable hyperbolic attractors.
