Incommensurate Fractional Discrete Neural Network: chaos and complexity

Abbes, Abderrahmane; Ouannas, Adel; Shawagfeh, Nabil; Khennaoui, Amina–Aicha

doi:10.1140/epjp/s13360-022-02472-6

Cited by 29 publications

(7 citation statements)

References 34 publications

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“…Scientists have been increasingly concerned about its applications in secure communication, neural networks, biology and other fields. Recently various complex dynamics are residing in fractional-order iterated map, such as chaos, hyperchaos and coexisting attractors [ 11 – 14 ]. For instance, in [ 15 ] Shukla et al explore the hyperchaotic dynamic of the fractional generalized Hénon map, whereas, in [ 16 ], the chaotic dynamics and combined synchronization of three two-dimensional maps have been investigated.…”

Section: Introductionmentioning

confidence: 99%

The fractional-order discrete COVID-19 pandemic model: stability and chaos

et al. 2022

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This paper presents and investigates a new fractional discrete COVID-19 model which involves three variables: the new daily cases, additional severe cases and deaths. Here, we analyze the stability of the equilibrium point at different values of the fractional order. Using maximum Lyapunov exponents, phase attractors, bifurcation diagrams, the 0-1 test and approximation entropy (ApEn), it is shown that the dynamic behaviors of the model change from stable to chaotic behavior by varying the fractional orders. Besides showing that the fractional discrete model fits the real data of the pandemic, the simulation findings also show that the numbers of new daily cases, additional severe cases and deaths exhibit chaotic behavior without any effective attempts to curb the epidemic.

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Section: Introductionmentioning

confidence: 99%

The fractional-order discrete COVID-19 pandemic model: stability and chaos

et al. 2022

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“…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]. For example, the coexisting chaos and hyperchaos in the fractional-order discrete SIE epidemic model have been analyzed in [23].…”

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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“…Thanks to these unique characteristics, fractional order iterated maps have been deeply studied in academic fields. [16][17][18] Macroeconomics is a field of economics concerned with the overall performance and behavior of an economy. It aims to achieve gross domestic product growth and price stability.…”

Section: Introductionmentioning

confidence: 99%

An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

Abbes

Ouannas²,

Shawagfeh³

2023

Chinese Phys. B

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This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order. The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically. In particular, the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior. Through using bifurcation diagrams, phase attractors, the maximum Lyapunov exponent and the 0–1 test, we verified that chaos exists in the new model with incommensurate fractional orders. Additionally, a complexity analysis is carried out utilizing the approximation entropy (ApEn) and C 0 complexity to prove that chaos exists. Finally, the main findings of this study are presented using numerical simulations.

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Incommensurate Fractional Discrete Neural Network: chaos and complexity

Cited by 29 publications

References 34 publications

The fractional-order discrete COVID-19 pandemic model: stability and chaos

The fractional-order discrete COVID-19 pandemic model: stability and chaos

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

An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

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