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

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.

arXiv comment18 pages, 16 pictures

References in corpus (2)

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

Cited by in corpus (4)

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• 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