Hidden homogeneous extreme multistability of a fractional-order hyperchaotic discrete-time system: chaos, initial offset boosting, amplitude control, control, and synchronization

Khennaoui, Amina Aicha, Ouannas, Adel, Bekiros, Stelios, Aly, Ayman A., Alotaibi, Ahmed, Jahanshahi, Hadi and Alsubaie, Hajid (2023) Hidden homogeneous extreme multistability of a fractional-order hyperchaotic discrete-time system: chaos, initial offset boosting, amplitude control, control, and synchronization. Symmetry, 15 (1). ISSN 2073-8994

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Abstract

Fractional order maps are a hot research topic; many new mathematical models are suitable for developing new applications in different areas of science and engineering. In this paper, a new class of a 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The hyperchaotic map has no equilibrium and lines of equilibrium points, depending on the values of the system parameters. All of the chaotic attractors generated by the proposed fractional map are hidden. The system dynamics are analyzed via bifurcation diagrams, Lyapunov exponents, and phase portraits for different values of the fractional order. The results show that the fractional map has rich dynamical behavior, including hidden homogeneous multistability and offset boosting. The paper also illustrates a novel theorem, which assures that two hyperchaotic fractional discrete systems achieve synchronized dynamics using very simple linear control laws. Finally, the chaotic dynamics of the proposed system are stabilized at the origin via a suitable controller.

Item Type:	Article
Official URL:	https://www.mdpi.com/journal/symmetry
Additional Information:	© 2023 The Authors
Divisions:	LSE Health
Subjects:	R Medicine > RA Public aspects of medicine > RA0421 Public health. Hygiene. Preventive Medicine Q Science > QA Mathematics Q Science > QC Physics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	14 Feb 2023 12:51
Last Modified:	12 Dec 2024 03:34
URI:	http://eprints.lse.ac.uk/id/eprint/118168

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