Global stability of local fractional Hénon-Lozi map using fixed point theory-Reference-Cited by-同舟云学术

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

Published:2022 Issue:6 Volume:7 Page:11399-11416
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ibrahim Rabha W.¹,Baleanu Dumitru²³⁴

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference35 articles.

1. M. Hénon, A two-dimensional mapping with a strange attractor, Commun.Math. Phys., 50 (1976), 69–77. http://dx.doi.org/10.1007/BF01608556

2. S. Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering, Boca Raton: CRC press, 2018.

3. Z. Elhadj, J. Sprott, A unified piecewise smooth chaotic mapping that contains the Hénon and the Lozi systems, Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, 1 (2011), 50–60.

4. A. Ouannas, A. Khennaoui, X. Wang, V. Pham, S. Boulaaras, S. Momani, Bifurcation and chaos in the fractional form of Hénon-Lozi type map, Eur. Phys. J. Spec. Top., 229 (2020), 2261–2273. http://dx.doi.org/10.1140/epjst/e2020-900193-4

5. K. Kolwankar, A. Gangal, Fractional differentiability of nowhere differentiable functions and dimensions, Chaos, 6 (1996), 505. http://dx.doi.org/10.1063/1.166197

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