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

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

2005-09-06

arxiv.org/abs/nlin/0509013v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, 16 pictures

Scientific paper

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 R\"{o}ssler oscillators is considered as an example.

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