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.

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

Modal Control of Linear Time-Invariant Discrete-Time Systems

1969 ◽  
Vol 2 (8) ◽  
pp. T133-T136 ◽  
Author(s):  
B. Porter ◽  
T. R. Crossley
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Feedback Loops ◽  
Modal Control ◽  
Discrete Time System ◽  
Linear Time Invariant ◽  
Modal Theory ◽  
Discrete Time Systems ◽  
Time Invariant ◽  
Time Systems

Modal control theory is applied to the design of feedback loops for linear time-invariant discrete-time systems. Modal theory is also used to demonstrate the explicit relationship which exists between the controllability of a mode of a discrete-time system and the possibility of assigning an arbitrary value to the eigenvalue of that mode.

scholarly journals A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 564 ◽  
Author(s):  
Jesus Munoz-Pacheco ◽  
Ernesto Zambrano-Serrano ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Equilibrium System ◽  
Hidden Attractors ◽  
Hidden Chaotic Attractor

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

CHAOTIFICATION OF DISCRETE-TIME SYSTEMS USING NEURONS

2004 ◽  
Vol 14 (04) ◽  
pp. 1405-1411 ◽  
Author(s):  
H. S. KWOK ◽  
WALLACE K. S. TANG
Keyword(s):  
Computer Simulations ◽  
Discrete Time ◽  
Activation Function ◽  
Feedback Signal ◽  
Discrete Time System ◽  
Hyperbolic Tangent ◽  
Time System ◽  
Discrete Time Systems ◽  
Arbitrary Dimensions ◽  
Time Systems

In this paper, a neuron is introduced for chaotifying nonchaotic discrete-time systems with arbitrary dimensions. By modeling the neuron with a hyperbolic tangent activation function, a scalar feedback signal expressed in a linear combination of the neuron outputs is used. Chaos can then be generated from the controlled discrete-time system. The existence of chaos is verified by both theoretical proof and computer simulations.

The MMVC for the Nth Order Linear Discrete-Time Systems under Prospective Strong Intervention

2014 ◽  
Vol 496-500 ◽  
pp. 1630-1633
Author(s):  
Qiu Ju Wang ◽  
Ru Dong Gai
Keyword(s):  
Discrete Time ◽  
System Model ◽  
Discrete Time System ◽  
Time System ◽  
Order Linear ◽  
First Order ◽  
Discrete Time Systems ◽  
Minimal Variance ◽  
Two Parameters ◽  
Time Systems

This paper is devoted to the issue of the modified minimal variance control (MMVC)for the nth linear discrete-time systems under prospective strong intervention (PSI). At fist, establish the Nth order linear discrete time system model. Based on the research of the first-order linear discrete time systems under PSI with the constraint of minimal variance control, the algorithm is extended to the nth order linear discrete time systems, so one can get MMVC of the nth order linear discrete-time systems with constraint under PSI and by introducing two parameters to proof.

scholarly journals HYPERCHAOTIC DYNAMICS OF A NEW FRACTIONAL DISCRETE-TIME SYSTEM

Fractals ◽  
2021 ◽  
pp. 2140034
Author(s):  
AMINA-AICHA KHENNAOUI ◽  
ADEL OUANNAS ◽  
SHAHER MOMANI ◽  
ZOHIR DIBI ◽  
GIUSEPPE GRASSI ◽  
...  
Keyword(s):  
Discrete Time ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Simulation Results ◽  
Time Systems ◽  
First Time

In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and [Formula: see text] complexity. Simulation results confirm the effectiveness of the approach illustrated herein.

Exponential Stability Analysis of Fixed Point Interfered Nonlinear Digital Systems in the Presence of Quantization and Overflow Constraints

2020 ◽  
Vol 19 (04) ◽  
pp. 2050040
Author(s):  
Saddam Hussain Malik ◽  
Muhammad Tufail ◽  
Muhammad Rehan ◽  
Shakeel Ahmed
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Digital Systems ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Digital Hardware ◽  
Time Systems

Finite word length is a practical limitation when discrete-time systems are implemented by using digital hardware. This restriction degrades the performance of a discrete-time system and may even lead it toward instability. This paper, addresses the stability and disturbance attenuation performance analysis of nonlinear discrete-time systems under the influence of energy-bounded external interferences when such systems are subjected to quantization and overflow effects of fixed point hardware. The proposed methodology, in comparison with previous paper, describes exponential stability for the nonlinear discrete-time systems by considering composite nonlinearities of digital hardware. The proposed criteria that ensure exponential stability and [Formula: see text] performance index for the digital systems under consideration are presented in the form of a set of linear matrix inequalities (LMIs) by exploiting Lyapunov stability theory, Lipschitz condition and sector conditions for different types of commonly used quantization and overflow arithmetic properties, and the results are validated for recurrent neural networks. Furthermore, novel stability analysis results for a nonlinear discrete-time system under hardware constraints can also be observed as a special case of the proposed criteria.

Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Othman Almatroud ◽  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Chaotic Dynamics ◽  
Approximate Entropy ◽  
Interesting Property ◽  
Chaotic Attractors ◽  
The Past ◽  
Offset Boosting ◽  
Discrete Time Systems ◽  
Infinite Line ◽  
Time Systems

Abstract The study of the chaotic dynamics in fractional-order discrete-time systems has received great attention in the past years. In this paper, we propose a new 2D fractional map with the simplest algebraic structure reported to date and with an infinite line of equilibrium. The conceived map possesses an interesting property not explored in literature so far, i.e., it is characterized, for various fractional-order values, by the coexistence of various kinds of periodic, chaotic and hyper-chaotic attractors. Bifurcation diagrams, computation of the maximum Lyapunov exponents, phase plots and 0–1 test are reported, with the aim to analyse the dynamics of the 2D fractional map as well as to highlight the coexistence of initial-boosting chaotic and hyperchaotic attractors in commensurate and incommensurate order. Results show that the 2D fractional map has an infinite number of coexistence symmetrical chaotic and hyper-chaotic attractors. Finally, the complexity of the fractional-order map is investigated in detail via approximate entropy.

scholarly journals Partitioning Technique for Relaxed Stability Criteria of Discrete-Time Systems with Interval Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Kuang-Yow Lian ◽  
Wen-Tsung Yang ◽  
Peter Liu
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Discrete Time System ◽  
Interval Time ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Varying Delay

We demonstrate an improved stability analysis based on a partition oriented technique for discrete-time systems with interval time-varying delay. The partition oriented technique introduces beneficial terms contributing to the negative definiteness of the Lyapunov function difference, meanwhile completely avoiding traditional inequality based approaches. In contrast, nonpartitioning oriented techniques do not put emphasis on further dividing the interval of the summation in the Lyapunov function. Herein, we demonstrate that the advantages of exploiting partitioning techniques manifest the relaxed stability criteria, as well as the flexibility to tune tradeoff between allowable timedelay range performance and computational load. Simulation carried out on a benchmark discrete-time system reveals the significant improvement in terms of maximum allowable upper bound in comparison.

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