  A feasible model is introduced that manifests phenomena intrinsic to
iterative complex analytic maps (such as the Mandelbrot set and Julia sets).
The system is composed of two coupled alternately excited oscillators (or
self-sustained oscillators). The idea is based on a turn-by-turn transfer of
the excitation from one subsystem to another (S.P.~Kuznetsov, Phys.~Rev.~Lett.
\bf 95 \rm, 2005, 144101) accompanied with appropriate nonlinear transformation
of the complex amplitude of the oscillations in the course of the process.
Analytic and numerical studies are performed. Special attention is paid to an
analysis of the violation of the applicability of the slow amplitude method
with the decrease in the ratio of the period of the excitation transfer to the
basic period of the oscillations. The main effect is the rotation of the
Mandelbrot-like set in the complex parameter plane; one more effect is the
destruction of subtle small-scale fractal structure of the set due to the
presence of non-analytic terms in the complex amplitude equations.
