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 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 New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

scholarly journals Numerical solution of a fractal-fractional order chaotic circuit system

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Abdon Atangana ◽  
Taseer Muhammad ◽  
Ebraheem Alzahrani
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Research Area ◽  
Fractional Operators ◽  
Chaotic Circuit ◽  
Order Model ◽  
Fractional Order Model ◽  
Chaotic Model ◽  
Important Research Area ◽  
Fractional Orders

The dynamical system has an important research area and due to its wide applications many researchers and scientists working to develop new model and techniques for their solution. We present in this work the dynamics of a chaotic model in the presence of newly introduced fractal-fractional operators. The model is formulated initially in ordinary differential equations and then we utilize the fractal-fractional (FF) in power law, exponential and Mittag-Leffler to generalize the model. For each fractal-fractional order model, we briefly study its numerical solution via the numerical algorithm. We present some graphical results with arbitrary order of fractal and fractional orders, and present that these operators provide different chaotic attractors for different fractal and fractional order values. The graphical results demonstrate the effectiveness of the fractal-fractional operators.

scholarly journals Complex dynamics behavior analysis of a new chaotic system based on fractional-order memristor

2021 ◽  
Vol 1861 (1) ◽  
pp. 012114
Author(s):  
Yongwei Qi ◽  
Chaojun Wu ◽  
Qi Zhang ◽  
Kai Yan ◽  
Haohan Wang
Keyword(s):  
Behavior Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Complex Dynamics ◽  
New Chaotic System

scholarly journals Controlling fractional-order new chaotic system based on Lyapunov equation

2010 ◽  
Vol 59 (3) ◽  
pp. 1524
Author(s):  
Xu Zhe ◽  
Liu Chong-Xin ◽  
Yang Tao
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Lyapunov Equation ◽  
New Chaotic System

scholarly journals Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 303 ◽  
Author(s):  
Khan Muhammad Altaf ◽  
Abdon Atangana
Keyword(s):  
Fractional Order ◽  
Order Parameter ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Disease Model ◽  
Numerical Approach ◽  
Fading Memory ◽  
Crossover Behavior ◽  
The World ◽  
Number Of Individuals

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior of such problems. In the case of Ebola, we observe spread that follows a fading memory process and also shows crossover behavior. Therefore, to capture this kind of spread one needs to use differential operators that posses crossover properties and fading memory. We analyze the Ebola disease model by considering three differential operators, that is the Caputo, Caputo–Fabrizio, and the Atangana–Baleanu operators. We present brief detail and some mathematical analysis for each operator applied to the Ebola model. We present a numerical approach for the solution of each operator. Further, numerical results for each operator with various values of the fractional order parameter α are presented. A comparison of the suggested operators on the Ebola disease model in the form of graphics is presented. We show that by decreasing the value of the fractional order parameter α , the number of individuals infected by Ebola decreases efficiently and conclude that for disease elimination, the Atangana–Baleanu operator is more useful than the other two.

A Novel Class of Chaotic Flows with Infinite Equilibriums and Their Application in Chaos-Based Communication Design Using DCSK

2018 ◽  
Vol 73 (7) ◽  
pp. 609-617 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Serdar Çiçek ◽  
Abdul Jalil M. Khalaf ◽  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
...  
Keyword(s):  
Chaotic System ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Engineering Application ◽  
Chaotic Flows ◽  
Fundamental Properties ◽  
New Chaotic System ◽  
Shift Keying ◽  
Chaos Shift Keying

AbstractDiscovering chaotic systems with interesting features has been of interest in the recent years. One such important and interesting feature is the type and shape of equilibrium points. We introduce a class of chaotic systems which could show different types of infinite equilibrium points. The fundamental properties of the proposed systems like bifurcation diagram and Lyapunov exponents are investigated. An electronic circuit of the presented chaotic systems is implemented. In addition, a chaos-based communication application by the differential chaos shift keying method with the new chaotic system is designed and tested for engineering application. According to the design test results, the proposed chaos-based communication system is successful. Therefore, the new chaotic system can be used in chaos-based communication systems.

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
Sign in / Sign up

Export Citation Format

Share Document