Fractional Maps and Fractional Attractors. Part II: Fractional Difference Caputo α- Families of Maps
DOI:
https://doi.org/10.5890/DNC.2015.11.003Abstract
In this paper we extend the notion of an α-family of maps to discrete systems defined by simple difference equations with the fractional Caputo difference operator. The equations considered are equivalent to maps with falling factorial-law memory which is asymptotically power-law memory. We introduce the fractional difference Universal, Standard, and Logistic α- Families of Maps and propose to use them to study general properties of discrete nonlinear systems with asymptotically power-law memory.References
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