A Fractional Model of Labyrinth Chaos and Numerical Analysis

Xin, Baogui; Ma, J-H.; Chen, T.; Yq, Liu

doi:10.1515/ijnsns.2010.11.10.837

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…There are several commonly used definitions of fractional order derivative [9,[11][12][13][14][15][16]. We utilize Caputo fractional order derivative in this paper.…”

Section: Fractional Order Calculusmentioning

confidence: 99%

“…Among them, Adams-Bashforth-Moulton (ABM) predictor-corrector approach has the merits of high precision and good stability, which was developed by Diethelm and other researchers [18,25,26] and successfully applied to many systems, such as [12,14,19,27]. We take a fractional differential equation with initial conditions:…”

Section: Predictor-corrector Approach For Fractional Order Calculusmentioning

confidence: 99%

“…In order to make a more simple and intuitive qualitative analysis of the character of solutions, the phase diagram [12,30,31] and time series graph [12,32,33] will be used to depict and analyse the dynamic process of the fractional order game model. …”

Section: The Fractional Order Game Model Of Colliery Safetymentioning

confidence: 99%

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A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Lu¹,

Wang²,

Dan³

2017

Mathematical Problems in Engineering

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Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.

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“…There are several commonly used definitions of fractional order derivative [9,[11][12][13][14][15][16]. We utilize Caputo fractional order derivative in this paper.…”

Section: Fractional Order Calculusmentioning

confidence: 99%

Section: Predictor-corrector Approach For Fractional Order Calculusmentioning

confidence: 99%

See 1 more Smart Citation

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Lu¹,

Wang²,

Dan³

2017

Mathematical Problems in Engineering

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“…15 Xin et al proposed a fractional model of Labyrinth chaos and they used modified Adams-Bashforth-Moultan numerical scheme for the solution of this model. 16 Götthans and Petrzela presented some numerical results about labyrinth chaotic system. 17 Sprott and Chlouverakis examined the details of this system including its route to chaos, attractor dimension, multistability, chaotic diffusion, and symbolic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Atangana–seda Numerical Scheme for Labyrinth Attractor With New Differential and Integral Operators

Atangana

Araz

2020

Fractals

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In this paper, we present a new numerical scheme for a model involving new mathematical concepts that are of great importance for interpreting and examining real world problems. Firstly, we handle a Labyrinth chaotic problem with fractional operators which include exponential decay, power-law and Mittag-Leffler kernel. Moreover, this problem is solved via Atangana-Seda numerical scheme which is based on Newton polynomial. The accuracy and efficiency of the method can be easily seen with numerical simulations.

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Dynamical Investigation of a Flexible Symmetry-Breaking Cyclic Chaotic Oscillator for Biomedical Image Encryption

Nzoulewa Dountsop,

Telem Kengou,

Kengne

2024

Braz J Phys

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A Fractional Model of Labyrinth Chaos and Numerical Analysis

Cited by 4 publications

References 18 publications

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Atangana–seda Numerical Scheme for Labyrinth Attractor With New Differential and Integral Operators

Dynamical Investigation of a Flexible Symmetry-Breaking Cyclic Chaotic Oscillator for Biomedical Image Encryption

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