On fractional-order symmetric oscillator with offset-boosting control

Xu, Changjin; Rahman, Mati ur; Băleanu, Dumitru

doi:10.15388/namc.2022.27.28279

Cited by 17 publications

(9 citation statements)

References 29 publications

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“…Offset boosting is an effective technique for shifting an attractor in phase space without changing the basic dynamics of a system [56][57][58][59][60][61][62].…”

Section: Offset Boosting For Symmetric Pairs Of Strange Attractorsmentioning

confidence: 99%

Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry

Jiang

et al. 2023

Symmetry

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A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications.

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“…Offset boosting is an effective technique for shifting an attractor in phase space without changing the basic dynamics of a system [56][57][58][59][60][61][62].…”

Section: Offset Boosting For Symmetric Pairs Of Strange Attractorsmentioning

confidence: 99%

Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry

Jiang

et al. 2023

Symmetry

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“…Fractional calculus has been used in many areas, such as mechanics, different kinds of physical waves, finance, neural networks, secure cryptography, autocontrol, etc. [29,30]. Recently, abundant studies on fractional dynamical models have been published.…”

Section: Introductionmentioning

confidence: 99%

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

Zhang,

2024

Fractal Fract

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In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order delay-coupled FitzHugh–Nagumo neural model is acquired. By designing a proper PDp controller, we can efficaciously control the stability domain and the time of emergence of the bifurcation phenomenon of the considered fractional delay-coupled FitzHugh–Nagumo neural model. By exploiting a reasonable hybrid controller, we can successfully adjust the stability domain and the bifurcation onset time of the involved fractional delay-coupled FitzHugh–Nagumo neural model. This study shows that when the delay crosses a critical value, a Hopf bifurcation will arise. When we adjust the control parameter, we can find other critical values to enlarge or narrow the stability domain of the fractional-order delay-coupled FitzHugh–Nagumo neural model. In order to check the correctness of the acquired outcomes of this article, we present some simulation outcomes via Matlab 7.0 software. The obtained theoretical fruits in this article have momentous theoretical significance in running and constructing networks.

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“…Numerous disciplines employ fractional analysis. The fractional differential operators Riemann-Liouville, Grunwald-Letnikov, Riesz, Hadamard, Caputo, Caputo-Fabrizio, etc., represent only some examples, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations

Moumen,

Mennouni,

Bouye

2023

Mathematics

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In this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Caputo fractional order for the first time. An efficient transformation reduces the problem to a system of two independent equations. Solving two algebraic equations yields an approximate solution to the problem. The proposed method’s efficiency and accuracy are validated. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests reinforce the interpretations of the theory.

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On fractional-order symmetric oscillator with offset-boosting control

Cited by 17 publications

References 29 publications

Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry

Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations

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