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

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 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.

Synchronization of a New Fractional Order Hyperchaotic System with Activation Feedback Control

2013 ◽  
Vol 397-400 ◽  
pp. 1278-1281
Author(s):  
Wei Wei Zhang ◽  
Ding Yuan Chen
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Current Paper ◽  
Hyperchaotic System ◽  
Fractional Order Systems ◽  
The Stability

In the current paper, a new fractional order hyperchaotic system is discussed. Using the activation feedback control, the synchronization of a new fractional order hyperchaotic system is implemented based on the stability theory of fractional order systems. Numerical simulations are demonstrated the effectiveness.

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.

Dynamics and Synchronization of the Fractional-Order Sprott E System

2013 ◽  
Vol 850-851 ◽  
pp. 876-879
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order Systems ◽  
The Stability

In this paper, dynamics and synchronization of the fractional-order Sprott E system are investigated. Firstly, the chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the synchronization of the system is realized. Numerical simulations are carried out to demonstrate the effectiveness of the controllers.

scholarly journals A New Scheme on Synchronization of Commensurate Fractional-Order Chaotic Systems Based on Lyapunov Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Hua Wang ◽  
Hang-Feng Liang ◽  
Peng Zan ◽  
Zhong-Hua Miao
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Equation ◽  
Practical Method ◽  
Fractional Order Systems ◽  
Model Uncertainties ◽  
External Disturbances ◽  
Zero Items

This paper proposes a new fractional-order approach for synchronization of a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. Combined with the fact that the states of the fractional chaotic systems are bounded, many coupled items can be taken as zero items. Then, the whole system can be simplified greatly and a simpler controller can be derived. Finally, the validity of the presented scheme is illustrated by numerical simulations of the fractional-order unified system.

SYNCHRONIZATION AND GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (13) ◽  
pp. 1695-1714 ◽  
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
State Observer ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
The Stability

In this paper, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given. Numerical simulations coincide with the theoretical analysis.

scholarly journals Combination Synchronization of Fractional Systems Involving the Caputo–Hadamard Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2781
Author(s):  
Abdelhameed M. Nagy ◽  
Abdellatif Ben Makhlouf ◽  
Abdulaziz Alsenafi ◽  
Fares Alazemi
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Fractional Systems ◽  
Combination Synchronization ◽  
Response System ◽  
Drive Systems ◽  
Scaling Matrix ◽  
Hadamard Derivative ◽  
Theoretical Results

The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one response system. We show that the combination synchronization phenomenon is achieved theoretically. Moreover, numerical simulations are carried out to confirm and validate the obtained theoretical results.

Synchronization of a Fractional-Order System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 796-799
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Stability

In this paper, synchronization of a fractional-order system with unknown parameters is studied. The chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, suitable synchronization controllers and parameter identification rules for the unknown parameters are designed. Numerical simulations are used to demonstrate the effectiveness of the controllers.

Control Fractional-Order Continuous Chaotic System via a Simple Fractional-Order Controller

2013 ◽  
Vol 336-338 ◽  
pp. 770-773
Author(s):  
Dong Zhang ◽  
Shou Liang Yang
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Stability Theorem ◽  
Asymptotically Stable ◽  
Fractional Order Systems ◽  
Control Scheme ◽  
The Stability ◽  
Fractional Order Controller ◽  
Order Continuous

A universal fractional-order controller is proposed to asymptotically stable the unstable equilibrium points and the nonequilibrium points of continuous fractional-order chaos systems. The simple fractional-order controller is obtained based on the stability theorem of nonlinear fractional-order systems. The control scheme is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed fractional-order controller.

Sign in / Sign up

Export Citation Format

Share Document