scholarly journals Chaos synchronization of fractional–order discrete–time systems with different dimensions using two scaling matrices

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 942-949 ◽  
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Amina–Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Xiong Wang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Strategies ◽  
Response System ◽  
Discrete Time Systems ◽  
Different Dimensions ◽  
Synchronization Scheme ◽  
Time Systems

Abstract In this paper, we study the synchronization of fractional–order discrete–time chaotic systems by means of two scaling matrices Θ and Φ. The considered synchronization scheme can be tailored to encompass several types of classical synchronization types. We proposed two nonlinear control strategies for the Θ–Φ synchronization of an m–dimensional drive system and an n–dimensional response system, whereby the synchronization dimension d = m and d = n, respectively. Numerical examples are presented to test the findings of the study.

scholarly journals On the Q–S Chaos Synchronization of Fractional-Order Discrete-Time Systems: General Method and Examples

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Adel Ouannas ◽  
Amina-Aicha Khennaoui ◽  
Giuseppe Grassi ◽  
Samir Bendoukha
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Control Strategies ◽  
Linearization Method ◽  
Discrete Time Systems ◽  
Control Scheme ◽  
The Stability ◽  
Time Systems ◽  
General Method

In this paper, we propose two control strategies for the Q–S synchronization of fractional-order discrete-time chaotic systems. Assuming that the dimension of the response system m is higher than that of the drive system n, the first control scheme achieves n-dimensional synchronization whereas the second deals with the m-dimensional case. The stability of the proposed schemes is established by means of the linearization method. Numerical results are presented to confirm the findings of the study.

scholarly journals Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

2019 ◽  
Vol 29 (1) ◽  
pp. 179-194 ◽  
Author(s):  
Said Djennoune ◽  
Maamar Bettayeb ◽  
Ubaid Muhsen Al-Saggaf
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Data Communication ◽  
Speech Communication ◽  
Discrete Time Systems ◽  
New Concepts ◽  
True State ◽  
Time Systems

Abstract This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.

On fractional–order discrete–time systems: Chaos, stabilization and synchronization

2019 ◽  
Vol 119 ◽  
pp. 150-162 ◽  
Author(s):  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Giuseppe Grassi ◽  
René Pierre Lozi ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Chaos Stabilization

EXPERIMENTAL RESULTS ON CHUA'S CIRCUIT ROBUST SYNCHRONIZATION VIA LMIs

2007 ◽  
Vol 17 (09) ◽  
pp. 3199-3209 ◽  
Author(s):  
C. D. CAMPOS ◽  
R. M. PALHARES ◽  
E. M. A. M. MENDES ◽  
L. A. B. TORRES ◽  
L. A. MOZELLI
Keyword(s):  
Discrete Time ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chua’S Oscillator ◽  
Laboratory Setup ◽  
Robust Synchronization ◽  
Discrete Time Systems ◽  
Main Ideas ◽  
Time Systems

This paper investigates the synchronization of coupled chaotic systems using techniques from the theory of robust [Formula: see text] control based on Linear Matrix Inequalities. To deal with the synchronization of a class of Lur'e discrete time systems, a project methodology is proposed. A laboratory setup based on Chua's oscillator circuit is used to demonstrate the main ideas of the paper in the context of the problem of information transmission.

scholarly journals STABILIZATION OF UNSTABLE PERIODIC ORBITS FOR DISCRETE TIME CHAOTIC SYSTEMS BY USING PERIODIC FEEDBACK

2006 ◽  
Vol 16 (02) ◽  
pp. 311-323 ◽  
Author(s):  
ÖMER MORGÜL
Keyword(s):  
Periodic Orbits ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Unstable Periodic Orbits ◽  
Discrete Time Systems ◽  
Feedback Scheme ◽  
Higher Dimensional ◽  
Periodic Feedback ◽  
Time Systems ◽  
Stability Results

We propose a periodic feedback scheme for the stabilization of periodic orbits for discrete time chaotic systems. We first consider one-dimensional discrete time systems and obtain some stability results. Then we extend these results to higher dimensional discrete time systems. The proposed scheme is quite simple and we show that any hyperbolic periodic orbit can be stabilized with this scheme. We also present some simulation results.

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (09) ◽  
pp. 1283-1292 ◽  
Author(s):  
MING-JUN WANG ◽  
XING-YUAN WANG
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Different Dimensions ◽  
The Stability ◽  
Synchronization Scheme

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme.

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