Qualitative study of the fractional order nonlinear chaotic model: electronic realization and secure data enhancement

2021 ◽  
Vol 78 (2) ◽  
pp. 93-108
Author(s):  
Najeeb Alam Khan ◽  
Saeed Akbar ◽  
Muhammad Ali Qureshi ◽  
Tooba Hameed ◽  
Nadeem Alam Khan
Keyword(s):  
Qualitative Study ◽  
Fractional Order ◽  
Chaotic Model ◽  
Secure Data

Quaternion anti-synchronization of a novel realizable fractional chaotic model

2021 ◽  
Vol 144 ◽  
pp. 110715
Author(s):  
Emad E. Mahmoud ◽  
M. Higazy ◽  
Hammad Alotaibi ◽  
S.M. Abo-Dahab ◽  
S. Abdel-Khalek ◽  
...  
Keyword(s):  
Chaotic Model

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

scholarly journals Time Evolution of Initial Errors in Lorenz’s 05 Chaotic Model

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Hynek Bednář ◽  
Aleš Raidl ◽  
Jiří Mikšovský
Keyword(s):  
Weather Prediction ◽  
Prediction Method ◽  
Atmospheric Model ◽  
Ensemble Prediction ◽  
Asymptotic Value ◽  
Time Limits ◽  
Initial Errors ◽  
Asymptotic Values ◽  
Chaotic Model ◽  
Almost All

Initial errors in weather prediction grow in time and, as they become larger, their growth slows down and then stops at an asymptotic value. Time of reaching this saturation point represents the limit of predictability. This paper studies the asymptotic values and time limits in a chaotic atmospheric model for five initial errors, using ensemble prediction method (model’s data) as well as error approximation by quadratic and logarithmic hypothesis and their modifications. We show that modified hypotheses approximate the model’s time limits better, but not without serious disadvantages. We demonstrate how hypotheses can be further improved to achieve better match of time limits with the model. We also show that quadratic hypothesis approximates the model’s asymptotic value best and that, after improvement, it also approximates the model’s time limits better for almost all initial errors and time lengths.

CHAOTIC INFLATIONARY SCENARIO IN BIANCHI TYPE I SPACETIME

2012 ◽  
Vol 27 (09) ◽  
pp. 1250049 ◽  
Author(s):  
RAJ BALI
Keyword(s):  
Energy Density ◽  
Bianchi Type ◽  
Type I ◽  
Inflationary Model ◽  
Bianchi Type I ◽  
Inflationary Scenario ◽  
Inflationary Phase ◽  
Chaotic Model ◽  
Frw Model ◽  
Frame Work

Chaotic inflationary model of the early universe proposed by Linde7 is investigated in the frame work of Bianchi type I spacetime. To determine inflationary scenario, we assume that scale factor [Formula: see text], λ being a constant, m the mass, V(ϕ) the potential energy density. It is shown that chaotic model leads to an inflationary phase which also helps in isotropization process. The Higg's field (ϕ) is initially large but decreases due to lapse of time in both cases. The assumption R3 = ABC~e3Ht does not lead to FRW model immediately but for large values of t, it reduces to FRW model since shear σ = 0 in FRW model and shear σ ≠ 0 in Bianchi type I model. The physical aspects of the model are also discussed.

scholarly journals Theory and applications of new fractional-order chaotic system under Caputo operator

2021 ◽  
Vol 12 (1) ◽  
pp. 20-38
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Caputo Derivative ◽  
Phase Portraits ◽  
Chaotic Circuit ◽  
Chaotic Model ◽  
The Stability ◽  
The Impact ◽  
Schematic Circuit ◽  
Good Agreement

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

scholarly journals A Transformed Lagged Ensemble Forecasting Technique for Increasing Ensemble Size

2007 ◽  
Vol 135 (4) ◽  
pp. 1424-1438 ◽  
Author(s):  
Andrew R. Lawrence ◽  
James A. Hansen
Keyword(s):  
Prediction Models ◽  
Weather Prediction ◽  
Ensemble Forecast ◽  
Ensemble Forecasting ◽  
Limited Area ◽  
Ensemble Size ◽  
Probabilistic Forecasting ◽  
Ensemble Forecasts ◽  
Chaotic Model ◽  
The Impact

Abstract An ensemble-based data assimilation approach is used to transform old ensemble forecast perturbations with more recent observations for the purpose of inexpensively increasing ensemble size. The impact of the transformations are propagated forward in time over the ensemble’s forecast period without rerunning any models, and these transformed ensemble forecast perturbations can be combined with the most recent ensemble forecast to sensibly increase forecast ensemble sizes. Because the transform takes place in perturbation space, the transformed perturbations must be centered on the ensemble mean from the most recent forecasts. Thus, the benefit of the approach is in terms of improved ensemble statistics rather than improvements in the mean. Larger ensemble forecasts can be used for numerous purposes, including probabilistic forecasting, targeted observations, and to provide boundary conditions to limited-area models. This transformed lagged ensemble forecasting approach is explored and is shown to give positive results in the context of a simple chaotic model. By incorporating a suitable perturbation inflation factor, the technique was found to generate forecast ensembles whose skill were statistically comparable to those produced by adding nonlinear model integrations. Implications for ensemble forecasts generated by numerical weather prediction models are briefly discussed, including multimodel ensemble forecasting.

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