Now showing items 1-4 of 4
On stability of fixed points and chaos in fractional systems.
In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2 . The method is tested on ...
On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations
(Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015)
In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is ...
Universal fractional map and cascade of bifurcations type attractors
(Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013-09)
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 ...
Caputo standard α-family of maps: Fractional difference vs. fractional
(Chaos: An Interdisciplinary Journal of Nonlinear Science, 2014-06)
In this paper, the author compares behaviors of systems which can be described by fractional differential and fractional difference equations using the fractional and fractional difference Caputo standard α-Families of ...