Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

doi:10.1088/1674-1056/ab820d

Abstract This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator. This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium. Through phase portrait, bifurcation diagrams, and largest Lyapunov exponents, it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors. Also, different tests are used to confirm the existence of chaos, such as 0-1 test and C₀ complexity. In addition, the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique. Furthermore, based on the fractional linearization method, a one-dimensional controller to stabilize the new system is proposed. Numerical results are presented to validate the findings of the paper.

Keywords: discrete chaos discrete fractional calculus hidden attractor

Received: 26 January 2020
Revised: 12 March 2020
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Ac	(Low-dimensional chaos)
	05.45.Gg	(Control of chaos, applications of chaos)
	05.30.Pr	(Fractional statistics systems)

Fund: The author Adel Ouannas was supported by the Directorate General for Scientific Research and Technological Development of Algeria. The author Shaher Momani was supported by Ajman University in UAE.

Corresponding Authors: Viet-Thanh Pham
E-mail: phamvietthanh@tdtu.edu.vn

Cite this article:

Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control 2020 Chin. Phys. B 29 050504

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Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

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