HYPERCHAOTIC DYNAMICS OF A NEW FRACTIONAL DISCRETE-TIME SYSTEM

Amina-Aicha Khennaoui (), Adel Ouannas, Shaher Momani, Zohir Dibi (), Giuseppe Grassi (), Dumitru Baleanu and Viet-Thanh Pham
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Amina-Aicha Khennaoui: Laboratory of Dynamical System and Control, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria
Adel Ouannas: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria3Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE4Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
Zohir Dibi: University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento 73100 Lecce, Italy
Dumitru Baleanu: Department of Mathematics, Cankaya University, 06530 Ankara, Turkey8Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan9Institute of Space Sciences, 76900 Magurele-Bucharest, Romania
Viet-Thanh Pham: 0Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-11

Abstract: 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 C0 complexity. Simulation results confirm the effectiveness of the approach illustrated herein.

Keywords: Chaos; Discrete Fractional Calculus; Hyperchaotic Map (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X2140034X

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