On possibility of realization of the Mandelbrot set in coupled continuous systems

2005/09/06 by О. Б. Исаева, O. B. Isaeva, Isaeva, O. B. +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #nlin.CD

paper · pdf · doi:10.48550/arxiv.nlin/0509013

18 pages, 16 pictures

arxiv created 2005/09/06 · openalex publication_date 2005/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

According to the method, suggested in our previous work (nlin/0509012) and based on the consideration of the specially coupled systems, the possibility of physical realization of the phenomena of complex analytic dynamics (such as Mandelbrot and Julia sets) is discussed. It is shown, that unlike the case of discrete maps or differential systems with periodic driving, investigated in mentioned work, there are some difficulties in attempts to obtain the Mandelbrot set for the coupled autonomous continuous systems. A system of coupled autonomous Rössler oscillators is considered as an example.

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• Phenomena of complex analytic dynamics in the systems of alternately excited coupled non-autonomous oscillators and self-sustained oscillators

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