Chaos and coexisting attractors in glucose-insulin regulatory system with incommensurate fractional-order derivatives

Debbouche, Nadjette; Almatroud, A. Othman; Ouannas, Adel; Batiha, Iqbal M.

doi:10.1016/j.chaos.2020.110575

Cited by 23 publications

(7 citation statements)

References 27 publications

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“…Fractional-order calculus can describe chaos and different nonlinear phenomena more accurately than integer-order derivatives. Recently, with the rapid progress of chaos theory and applied research, fractional-order chaotic systems [1][2][3][4][5][6][7][8][9] have received wide attention and undergone rapid development. Yuan et al [2] studied chaos and the bifurcation of fractional semi-logistic maps based on the Lyapunov exponent, the Schwarzian derivative, Shannon entropy and Kolmogorov entropy.…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Financial System and Fixed-Time Synchronization

Peng

Zheng

2022

Fractal Fract

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This study is concerned with the dynamic investigation and fixed-time synchronization of a fractional-order financial system with the Caputo derivative. The rich dynamic behaviors of the fractional-order financial system with variations of fractional orders and parameters are discussed analytically and numerically. Through using phase portraits, bifurcation diagrams, maximum Lyapunov exponent diagrams, 0–1 testing and time series, it is found that chaos exists in the proposed fractional-order financial system. Additionally, a complexity analysis is carried out utilizing approximation entropy SE and C0 complexity to detect whether chaos exists. Furthermore, a synchronization controller and an adaptive parameter update law are designed to synchronize two fractional-order chaotic financial systems and identify the unknown parameters in fixed time simultaneously. The estimate of the setting time of synchronization depends on the parameters of the designed controller and adaptive parameter update law, rather than on the initial conditions. Numerical simulations show the effectiveness of the theoretical results obtained.

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Section: Introductionmentioning

confidence: 99%

Fractional-Order Financial System and Fixed-Time Synchronization

Peng

Zheng

2022

Fractal Fract

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“…Fractional calculus is a significant tool for mathematical modeling of numerous issues in physics and mathematics. Discrete fractional calculus has drawn the interest of a great number of researchers during the last several years [8][9][10][11][12], and they have been increasingly interested in its potential applications in neural networks, secure communication, biology, and other domains [13][14][15]. Recently numerous different dynamics including chaos, hyperchaos and coexisting attractors in fractional-order systems have been explored [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Hidden multistability of fractional discrete non-equilibrium point memristor based map

et al. 2023

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At present, the multistability analysis in discrete nonlinear fractional-order systems is a subject that is receiving a lot of attention. In this article, a new discrete non-equilibrium point memristor-based map with $\gamma-th$ Caputo fractional difference is introduced. In addition, in the context of the commensurate and non-commensurate instances, the non-linear dynamics of the suggested discrete fractional map, such as its multistability, hidden chaotic attractor, and hidden hyperchaotic attractor, are investigated through several numerical techniques, including Lyapunov exponents, phase attractors, bifurcation diagrams, and the $0–1$ test. This dynamic behaviors suggests that the fractional discrete memristive map has a hidden multistability. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy ($ApEn$) and the $C_0$ measure. The findings show that the model has a high degree of complexity, which is affected by the system parameters and the fractional values.

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“…For instance in [13], a non-equilibrium chaotic system was investigated in view of commensurate and incommensurate fractional orders and with only one signum function, and it has been shown accordingly that the considered system can display several complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. In [14], the effect of the incommensurate fractional-order derivatives on a glucose-insulin regulatory model was analyzed, and some interesting dynamics, such as chaos, hidden and coexisting attractors were consequently generated from such model. For additional literature, the reader may refer to references [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A new two-dimensional fractional discrete rational map: chaos and complexity

Shatnawi¹,

Abbes²,

Ouannas³

et al. 2022

Phys. Scr.

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In this paper, a new two-dimensional fractional discrete rational map with γth-Caputo fractional difference operator is introduced. The study of the presence and stability of the equilibrium points shows that there are four types of equilibrium points; no equilibrium point, a line of equilibrium points, one equilibrium point and two equilibrium points. In addition, in the context of the commensurate and incommensurate instances, the nonlinear dynamics of the suggested fractional discrete map in different cases of equilibrium points are investigated through several numerical techniques including Lyapunov exponents, phase attractors and bifurcation diagrams. These dynamic behaviors suggest that the fractional discrete rational map has both hidden and self-excited attractors, which have rarely been described in the literature. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy (ApEn) and the C0-measure.

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Chaos and coexisting attractors in glucose-insulin regulatory system with incommensurate fractional-order derivatives

Cited by 23 publications

References 27 publications

Fractional-Order Financial System and Fixed-Time Synchronization

Fractional-Order Financial System and Fixed-Time Synchronization

Hidden multistability of fractional discrete non-equilibrium point memristor based map

A new two-dimensional fractional discrete rational map: chaos and complexity

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