Open AccessHYPERCHAOTIC DYNAMICS OF A NEW FRACTIONAL DISCRETE-TIME SYSTEM
Author(s) -
Amina–Aicha Khennaoui,
Adel Ouannas,
Shaher Momani,
Z. Dibi,
Giuseppe Grassi,
Dumitru Băleanu,
Viet–Thanh Pham
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x2140034x
Subject(s) - lyapunov exponent , phase portrait , discrete time and continuous time , nonlinear system , mathematics , logistic map , computation , bifurcation , complex dynamics , statistical physics , computer science , chaotic , mathematical analysis , algorithm , physics , artificial intelligence , statistics , quantum mechanics
In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and [Formula: see text] complexity. Simulation results confirm the effectiveness of the approach illustrated herein.