A physical interpretation of fractional-order-derivatives in a jerk system: Electronic approach

Echenausía-Monroy, J.L.; Gilardi-Velázquez, H. E.; Jaimes-Reátegui, R.; Aboites, Vicente; Huerta-Cuéllar, G.

doi:10.1016/j.cnsns.2020.105413

Cited by 26 publications

(20 citation statements)

References 45 publications

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“…e term (π/2M) − min i |arg(λ i )| is called the Instability Measure for equilibrium points in Fractional Order Systems (IMFOS). is measure is a necessary [47], but not a sufficient condition for the presence of chaos in a fractional order system [52][53][54].…”

Section: Definitions and Lemmamentioning

confidence: 99%

Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode

et al. 2021

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In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.13 for the incommensurate order case. Also, period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results.

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Section: Definitions and Lemmamentioning

confidence: 99%

Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode

et al. 2021

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“…To attain the complete range of the signal's linear transformations, the offset boosting can be set together with the so-called amplitude control. It appeared that a novel boosting controller, which was introduced by [20], can destroy the symmetry of the variableboostable system [36,37]. In this section, we introduce three additional controlled constants η, ω, and in accordance with the variables x, y, and z, respectively.…”

Section: Variable-boostable Hidden Attractors Of Commensurate and Incmentioning

confidence: 99%

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

Debbouche

Momani

Ouannas

et al. 2021

Entropy

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This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.

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“…An interesting procedure of comparison between the geometry of the attractors can be found in [24]. e method consists of comparing the amplitude of the attractors in different orders of the Caputo derivative.…”

Section: Illustration Of the Numerical Schemementioning

confidence: 99%

“…e comparison of the attractors' geometry at the orders α � 0.9 and α � 0.95 can be analyzed for model (7). We adopt the sketch presented in [24]. We consider the phase portraits in plane (x, y) in Figures 1 and 2 and construct polygons, calculate their areas, and compare them.…”

Section: Illustration Of the Numerical Schemementioning

confidence: 99%

Study of a Fractional‐Order Chaotic System Represented by the Caputo Operator

Sene

2021

Complexity

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This paper is presented on the theory and applications of the fractional-order chaotic system described by the Caputo fractional derivative. Considering the new fractional model, it is important to establish the presence or absence of chaotic behaviors. The Lyapunov exponents in the fractional context will be our fundamental tool to arrive at our conclusions. The variations of the model’s parameters will generate chaotic behavior, in general, which will be established using the Lyapunov exponents and bifurcation diagrams. For the system’s phase portrait, we will present and apply an interesting fractional numerical discretization. For confirmation of the results provided in this paper, the circuit schematic is drawn and simulated. As it will be observed, the results obtained after the simulation of the numerical scheme and with the Multisim are in good agreement.

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A physical interpretation of fractional-order-derivatives in a jerk system: Electronic approach

Cited by 26 publications

References 45 publications

Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode

Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

Study of a Fractional‐Order Chaotic System Represented by the Caputo Operator

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