A quadratic fractional map without equilibria: Bifurcation, 0–1 test, complexity, entropy, and control

Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Giuseppe Grassi, Viet Thanh Pham, Reyad El-Khazali, Duy Vo Hoang

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

Fractional calculus in discrete-time systems is a recent research topic. The fractional maps introduced in the literature often display chaotic attractors belonging to the class of “self-excited attractors”. The field of fractional map with “hidden attractors” is completely unexplored. Based on these considerations, this paper presents the first example of fractional map without equilibria showing a number of hidden attractors for different values of the fractional order. The presence of the chaotic hidden attractors is validated via the computation of bifurcation diagrams, maximum Lyapunov exponent, 0–1 test, phase diagrams, complexity, and entropy. Finally, an active controller with the aim for stabilizing the proposed fractional map is successfully designed.

Original languageBritish English
Article number748
JournalElectronics (Switzerland)
Volume9
Issue number5
DOIs
StatePublished - May 2020

Keywords

  • Chaos
  • Control
  • Hidden attractors

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