  We consider a self-oscillator whose excitation parameter is varied. Frequency
of the variation is much smaller then the natural frequency of the oscillator
so that oscillations in the system are periodically excited and decay. Also a
time delay as added such that when the oscillations start to grow at a new
excitation stage they are influenced via the delay line by the oscillations at
the penultimate excitation stage. Due to a nonlinearity the seeding from the
past arrives with a doubled phase so that oscillation phase changes from stage
to stage according to chaotic Bernoulli-type map. As a result, the system
operates as two coupled hyperbolic chaotic subsystems. Varying the relation
between the delay time and the excitation period we affect a coupling strength
between these subsystems as well as intensity of the phase doubling mechanism
responsible for the hyperbolicity. Due to this, a transition from
non-hyperbolic to hyperbolic hyperchaos occurs. The following steps of the
transition scenario are revealed and analyzed: (a) an intermittency as
alternation of long staying near a fixed point at the origin and short chaotic
bursts; (b) chaotic oscillations with often visits to the fixed point; (c)
plain hyperchaos without hyperbolicity after termination visiting the fixed
point; (d) transformation of hyperchaos to hyperbolic form.
