On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory

L.F. Ávalos-Ruiz, J.F. Gómez-Aguilar, A. Atangana and Kolade M. Owolabi

Chaos, Solitons & Fractals, 2019, vol. 127, issue C, 364-388

Abstract: In this paper, we propose a fractional form of two-dimensional generalized mythical bird, butterfly wings and paradise bird maps involving the fractional conformable derivative of Khalil’s and Atangana’s type, the Liouville–Caputo and Atangana–Baleanu derivatives with constant and variable-order. We obtain new chaotical behaviors considering numerical schemes based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. Also, the dynamics of the proposed maps are investigated numerically through phase plots considering combinations of these derivatives and mixed integration methods for each map. The numerical simulations show very strange and new behaviors for the first time in this manuscript.

Keywords: Fractional calculus; Variable-order fractional operators; Chaotical maps; Mixed schemes (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:127:y:2019:i:c:p:364-388

DOI: 10.1016/j.chaos.2019.07.010

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