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Keywords = Lorenz-Stenflo system

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15 pages, 2338 KiB  
Article
A Comparative Study and Numerical Solutions for the Fractional Modified Lorenz–Stenflo System Using Two Methods
by Mohamed Elbadri, Mohamed A. Abdoon, Abdulrahman B. M. Alzahrani, Rania Saadeh and Mohammed Berir
Axioms 2025, 14(1), 20; https://doi.org/10.3390/axioms14010020 - 30 Dec 2024
Cited by 2 | Viewed by 722
Abstract
This paper provides a solution to the new fractional-order Lorenz–Stenflo model using the adaptive predictor–corrector approach and the ρ-Laplace New Iterative Method (LρNIM), representing an extensive comparison between both techniques with RK4 related to accuracy and [...] Read more.
This paper provides a solution to the new fractional-order Lorenz–Stenflo model using the adaptive predictor–corrector approach and the ρ-Laplace New Iterative Method (LρNIM), representing an extensive comparison between both techniques with RK4 related to accuracy and error analysis. The results show that the suggested approaches allow one to be more accurate in analyzing the dynamics of the system. These techniques also produce results that are comparable to the results of other approximate techniques. The techniques can, thus, be used on a wider class of systems in order to provide more accurate results. These techniques also appropriately identify chaotic attractors in the system. These techniques can be applied to solve various numerical problems arising in science and engineering in the future. Full article
(This article belongs to the Special Issue Fractional Differential Equation and Its Applications)
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12 pages, 1640 KiB  
Article
Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity
by Chih-Hsueh Lin, Guo-Hsin Hu and Jun-Juh Yan
Mathematics 2020, 8(3), 327; https://doi.org/10.3390/math8030327 - 3 Mar 2020
Cited by 7 | Viewed by 2312
Abstract
In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is [...] Read more.
In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is designed such that the controlled dynamics in the sliding manifold becomes easy to analyze. Furthermore, only by using single rippling SMC even with input nonlinearity can we ensure the existence of the sliding mode for the controlled dynamics and suppress the chaotic behavior in a manner of rippling. Under the proposed control scheme, the chaos behavior in uncertain generalized 4D Lorenz–Stenflo systems subjected to mismatched uncertainties can be robustly suppressed to predictable bounds, which is not addressed in the literature. The numerical simulation results including matched/mismatched uncertainties and nonlinear inputs are presented to verify the robustness and validity of the rippling sliding mode controller. Full article
(This article belongs to the Special Issue Robust Stabilization of Linear and Nonlinear Systems)
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9 pages, 1489 KiB  
Article
Complex Dynamical Behaviors of Lorenz-Stenflo Equations
by Fuchen Zhang and Min Xiao
Mathematics 2019, 7(6), 513; https://doi.org/10.3390/math7060513 - 5 Jun 2019
Cited by 8 | Viewed by 2809
Abstract
A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that [...] Read more.
A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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