  The possibility of realization of the phenomena of complex analytic dynamics
for the realistic physical models are investigated. Observation of the
Mandelbrot and Julia sets in the parameter and phase spaces both for the
discrete maps and non-autonomous continuous systems is carried out. For these
purposes, the method, based on consideration of coupled systems, demonstrating
period-doubling cascade is suggested. Novel mechanism of synchronization loss
in coupled systems corresponded to the dynamical behavior intrinsic to the
complex analytic maps is offered.
