Global stability of local fractional Hénon-Lozi map using fixed point theory

Rabha W. Ibrahim; Dumitru Baleanu; Rabha W. Ibrahim; Dumitru Baleanu

doi:10.3934/math.2022636

AIMS Mathematics

2022, Volume 7, Issue 6: 11399-11416. doi: 10.3934/math.2022636

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Global stability of local fractional Hénon-Lozi map using fixed point theory

Rabha W. Ibrahim ^{1
,
,},
Dumitru Baleanu ^2,3,4

1.
The Institute of Electrical and Electronics Engineers (IEEE): 94086547
2.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
3.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 03 February 2022 Revised: 06 March 2022 Accepted: 13 March 2022 Published: 12 April 2022
MSC : 28D37, 30D05

We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.
- fractional calculus,
- differential operator,
- fractional differential equation,
- fractal chaotic,
- fractal
Citation: Rabha W. Ibrahim, Dumitru Baleanu. Global stability of local fractional Hénon-Lozi map using fixed point theory[J]. AIMS Mathematics, 2022, 7(6): 11399-11416. doi: 10.3934/math.2022636

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Abstract

We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.

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