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

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