On possibility of realization of the phenomena of complex analytic dynamics in physical systems. Novel mechanism of the synchronization loss in coupled period-doubling systems

摘要

The possibility of realization of the phenomena of complex analytic dynamicsfor the realistic physical models are investigated. Observation of theMandelbrot and Julia sets in the parameter and phase spaces both for thediscrete maps and non-autonomous continuous systems is carried out. For thesepurposes, the method, based on consideration of coupled systems, demonstratingperiod-doubling cascade is suggested. Novel mechanism of synchronization lossin coupled systems corresponded to the dynamical behavior intrinsic to thecomplex analytic maps is offered.