Fractional Maps and Fractional Attractors. Part II: Fractional Difference $\alpha$-Families of Maps

Mark Edelman

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arXiv · 1404.4906

Fractional Maps and Fractional Attractors. Part II: Fractional Difference $\alpha$-Families of Maps

Mark Edelman

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Abstract

In this paper we extend the notion of an $\alpha$-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 $\alpha$-Families of Maps and propose to use them to study general properties of discrete nonlinear systems with asymptotically power-law memory.

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Mark Edelman. 2014-04-19. Fractional Maps and Fractional Attractors. Part II: Fractional Difference $\alpha$-Families of Maps. https://arxiv.org/abs/1404.4906

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