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

Abstract

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.

arXiv comment14 pages, 9 figures

References in corpus (1)

• Mandelbrot set in coupled logistic maps and in an electronic experiment

Cited by in corpus (4)

• On possibility of realization of the Mandelbrot set in coupled continuous systems
• Siegel disk for complexified Henon map
• Phenomena of complex analytic dynamics in the systems of alternately excited coupled non-autonomous oscillators and self-sustained oscillators
• Phenomena of complex analytic dynamics in the non-autonomous, nonlinear ring system