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

scholarly journals Puu System of Fractional Order and Its Chaos Suppression

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 340 ◽  
Author(s):  
Marius-F. Danca
Keyword(s):  
Periodic Solutions ◽  
Fractional Order ◽  
Discrete Time ◽  
Continuous Time ◽  
Control Algorithm ◽  
Chaos Control ◽  
Chaos Suppression ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Order Continuous

In this paper, the fractional-order variant of Puu’s system is introduced, and, comparatively with its integer-order counterpart, some of its characteristics are presented. Next, an impulsive chaos control algorithm is applied to suppress the chaos. Because fractional-order continuous-time or discrete-time systems have not had non-constant periodic solutions, chaos suppression is considered under some numerical assumptions.

scholarly journals An Unprecedented 2-Dimensional Discrete-Time Fractional-Order System and Its Hidden Chaotic Attractors

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Amina Aicha Khennaoui ◽  
A. Othman Almatroud ◽  
Adel Ouannas ◽  
M. Mossa Al-sawalha ◽  
Giuseppe Grassi ◽  
...  
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Test Method ◽  
Order System ◽  
Chaotic Attractors ◽  
Discrete Time System ◽  
Discrete Time Systems ◽  
Time Systems

Some endeavors have been recently dedicated to explore the dynamic properties of the fractional-order discrete-time chaotic systems. To date, attention has been mainly focused on fractional-order discrete-time systems with “self-excited attractors.” This paper makes a contribution to the topic of fractional-order discrete-time systems with “hidden attractors” by presenting a new 2-dimensional discrete-time system without equilibrium points. The conceived system possesses an interesting property not explored in the literature so far, i.e., it is characterized, for various fractional-order values, by the coexistence of various kinds of chaotic attractors. Bifurcation diagrams, computation of the largest Lyapunov exponents, phase plots, and the 0-1 test method are reported, with the aim to analyze the dynamics of the system, as well as to highlight the coexistence of chaotic attractors. Finally, an entropy algorithm is used to measure the complexity of the proposed system.

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 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.

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