Clocking convergence of the fractional difference logistic map

Abstract

The convergence of the fractional difference logistic map is studied in this paper. A computational technique based on the visualisation of the algebraic complexity of transient processes is employed for that purpose. It is demonstrated that the dynamics of the fractional difference logistic map is similar to the behaviour of the extended invertible logistic map in the neighbourhood of unstable orbits. This counter-intuitive result provides a new insight into the transient processes of the fractional difference logistic map.

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Correspondence to Minvydas Ragulskis.

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Petkevičiūtė-Gerlach, D., Timofejeva, I. & Ragulskis, M. Clocking convergence of the fractional difference logistic map. Nonlinear Dyn 100, 3925–3935 (2020). https://doi.org/10.1007/s11071-020-05703-6

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Keywords

  • Fractional difference logistic map
  • Convergence
  • H-rank
  • Temporal stabilisation