Please use this identifier to cite or link to this item:
https://hdl.handle.net/20.500.12202/50
Title: | Universal fractional map and cascade of bifurcations type attractors |
Authors: | Edelman, Mark 0000-0002-5190-3651 |
Keywords: | chaotic dynamics attractors bifurcations integral equations Integrodifferential equations nanomaterial properties anatomy human memory chaos nonlinear dynamics |
Issue Date: | Sep-2013 |
Publisher: | Chaos: An Interdisciplinary Journal of Nonlinear Science |
Citation: | Edelman, Mark. (2013) Universal fractional map and cascade of bifurcations type attractors. Chaos 23. |
Abstract: | We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional α<2 in the area of parameter values of the transition through the period doubling cascade of bifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors—cascade of bifurcations type trajectories. |
URI: | https://doi.org/10.1063/1.4819165 https://hdl.handle.net/20.500.12202/50 |
ISSN: | 1089-7682 |
Appears in Collections: | Stern College for Women -- Faculty Publications |
Files in This Item:
File | Description | Size | Format | |
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Edelman Universal fractional 2013 Chaos.pdf | 4.81 MB | Adobe PDF | View/Open |
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