scholarly journals One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order1

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Zhou ◽  
Rongji Bai
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Result ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Lorenz Chaotic System

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in1<q<2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order1<q<2is considered. Numerical simulations show the validity and feasibility of the proposed scheme.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

scholarly journals Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Equilibrium Points ◽  
Order Derivative ◽  
Fractional Order Systems ◽  
Fractional Order Derivative ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

scholarly journals Adaptive synchronization of a class of fractional order chaotic system with uncertain parameters

2015 ◽  
Vol 11 (6) ◽  
pp. 5306-5316
Author(s):  
De-fu Kong
Keyword(s):  
Parameter Identification ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Criterion ◽  
Local Stability ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Control Scheme

In this manuscript, the adaptive synchronization of a class of fractional order chaotic system with uncertain parameters is studied. Firstly, the local stability of the fractional order chaotic system is analyzed using fractional stability criterion. Then, based on the J function criterion, suitable adaptive synchronization controller and parameter identification rules of the unknown parameters are investigated. Finally, the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

Adaptive Synchronization of the Fractional-Order Sprott N System

2013 ◽  
Vol 850-851 ◽  
pp. 872-875
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Phase Plane ◽  
Adaptive Synchronization ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
The Stability

In this paper, adaptive synchronization of the fractional-order Sprott N system is investigated. Firstly, the chaotic attractors on different phase plane of the system are got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the adaptive synchronization of the system is realized. Numerical simulations are used to demonstrate the effectiveness for the controllers.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

scholarly journals Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 102093-102105 ◽  
Author(s):  
Amr M. Abdelaty ◽  
Merna Roshdy ◽  
Lobna A. Said ◽  
Ahmed G. Radwan
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Product Integration ◽  
Integration Rules

scholarly journals Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jian-Bing Hu ◽  
Ling-Dong Zhao
Keyword(s):  
Fractional Calculus ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Fractional Differentiation ◽  
Fractional Chaotic System

We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectiveness of the method.

Investigation of Synchronization for a Fractional-Order Delayed System

2014 ◽  
Vol 687-691 ◽  
pp. 447-450 ◽  
Author(s):  
Hong Gang Dang ◽  
Wan Sheng He ◽  
Xiao Ya Yang
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Fractional Order Systems ◽  
Delayed System ◽  
The Stability

In this paper, synchronization of a fractional-order delayed system is studied. Based on the stability theory of fractional-order systems, by designing appropriate controllers, the synchronization for the proposed system is achieved. Numerical simulations show the effectiveness of the proposed scheme.

scholarly journals High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3130
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed
Keyword(s):  
Equilibrium Point ◽  
Image Encryption ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Unstable Equilibrium ◽  
Phase Portraits ◽  
Time Efficiency ◽  
Unstable Equilibrium Point

Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

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