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

TL;DR

This paper explores how complex analytic dynamics phenomena, like Mandelbrot and Julia sets, can be realized in physical systems, introducing a new mechanism for synchronization loss in coupled period-doubling systems.

Contribution

It demonstrates the realization of complex analytic dynamics in realistic physical models and proposes a novel mechanism for synchronization loss in coupled systems.

Findings

Observation of Mandelbrot and Julia sets in physical models

Introduction of a new synchronization loss mechanism

Application to 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.