The possibility of realization of the phenomena of complex analytical dynamics for the realistic physical systems is investigated. Observation of the Mandelbrot and Julia sets in the parameter and phase spaces both for the discrete mappings and continuous systems is carried out. For these purposes, in present work the method is suggested, based on consideration of coupled systems, where the subsystems demonstrate perioddoublinges cathcad. So, Henon mapping, quadratic oscillator with harmonic driving force and autonomous Rossler oscillator are considered as subsystems. The relations between phenomena of complex analytical dynamics and problems of synchronization loss are discussed.