scholarly journals Studying the Chaotic Dynamics Using Rossler-Chua Systems Combined with A Semiconductor Laser

2021 ◽  
pp. 2213-2221
Author(s):  
Raied K. Jamal ◽  
Falah H. Ali ◽  
Falah A-H. Mutlak
Keyword(s):  
Time Series ◽  
Semiconductor Laser ◽  
Dynamic Systems ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Chaotic Dynamic ◽  
Secure Communications ◽  
Wide Field ◽  
New Chaotic System

     In this paper, two different chaotic dynamic systems are coupled using a semiconductor laser to produce a new chaotic system. These two chaotic systems are Rossler and Chua systems. X-dynamic of Rossler system was coupled optically using optical fiber as a carrier of signal with x, y, and z-dynamics of Chua system. The results were analyzed and the behavior of Chua system was found to be changing in time series which, in turn, changed the attractor. The Chua attractor was converted from double scroll to single scroll. The results obtained from connecting two different systems in chaotic behavior showed a remarkable increase in the bandwidth of Chua system. This increase in bandwidth opens up a wide field for many applications, the most important of which is in the field of secure communications.

scholarly journals S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium

2019 ◽  
Vol 9 (4) ◽  
pp. 781 ◽  
Author(s):  
Xiong Wang ◽  
Ünal Çavuşoğlu ◽  
Sezgin Kacar ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Image Encryption Algorithm

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.

scholarly journals A New 4-D Chaotic System with Hidden Attractor and its Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1245 ◽  
Author(s):  
Aceng Sambas ◽  
Mustafa Mamat ◽  
Sundarapandian Vaidyanathan ◽  
Muhammad Mohamed ◽  
Mada Sanjaya
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Hidden Attractor ◽  
Circuit Realization ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
Work First

In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.

scholarly journals Generating a New Chaotic System Using Two Chaotic Rossler-Chua Coupling Systems

2021 ◽  
Author(s):  
Ryam Salam Abdulaali ◽  
Raied K. Jamal ◽  
Salam K. Mousa
Keyword(s):  
Time Series ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Matlab Program ◽  
Rossler System ◽  
New Chaotic System ◽  
Rössler System ◽  
New System

Abstract It is proposed in this paper that a new chaotic system may be formed by combining two distinct chaotic systems, such as the Rossler system and the Chua system, in which the x dynamic of the Rossler system is linked with the z dynamic of the Chua system, results in a new chaotic system. Some of the basic dynamic behavior is explored and examined for new system by using the Matlab program. They noticed that it was a difference in the time series of the Chua system and this in turn led to a difference in the attractor, as the attractor of the Chua system changed from double scroll to single scroll and this led to change of the bandwidth of the Chua system, meaning that the Rӧssler system affected the Chua system, which led to an increase in the possibility of using this system in secret communications.

Experimental evidence of Phase Control method in chaotic Semiconductor Laser

2019 ◽  
pp. 1469-1477
Author(s):  
Raghad I. Ibrahim ◽  
Kais A. M. Al Naimee ◽  
Sameer Kh. Yaseen
Keyword(s):  
Time Series ◽  
Semiconductor Laser ◽  
Control Method ◽  
Chaotic Behavior ◽  
External Perturbation ◽  
Phase Control ◽  
Driving Frequency ◽  
Regular Behavior ◽  
Laser Dynamics ◽  
Excitable Systems

we study how to control the dynamics of excitable systems by using the phase control technique.We study how to control nonlinear semiconductor laser dynamics with optoelectronic feedback using the phase control method. The phase control method uses the phase difference between a small.added frequenc y and the main driving frequency to suppress chaos, which leads to various periodic orbits. The experimental studying for the evaluation of chaos modulation behavior are considered in two conditions, the first condition, when one frequency of the external perturbation is varied, secondly, when two of these perturbations are changed. The chaotic system becomes regular under one frequency or two frequencies, But in two frequencies, phase control showed an excellent ability to maintain regular behavior in chaotic window and reexcite chaotic behavior when destroyed. This dynamics of the laser output are analyzed by time series and bifurcation diagram.

On Fuzzy Control of Chaotic Systems

2004 ◽  
Vol 10 (7) ◽  
pp. 979-993 ◽  
Author(s):  
Ahmad M. Harb ◽  
Issam A. Smadi
Keyword(s):  
Mathematical Model ◽  
Fuzzy Logic ◽  
Fuzzy Control ◽  
Power Systems ◽  
Strange Attractor ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Secure Communications ◽  
Nonlinear Controllers ◽  
Linear And Nonlinear

In this paper, we introduce the control of the strange attractor, chaos. Because of the importance of controlling undesirable behavior in systems. researchers are investigating the use of linear and nonlinear controllers, either to remove such oscillations (in power systems) or to match two chaotic systems (in secure communications). The idea of using the fuzzy logic concept for controlling chaotic behavior is presented. There are two good reasons for using fulzy control: first, there is no mathematical model available for the process; secondly. it can satisfy nonlinear control that can be developed empirically. without complicated mathematics. The two systems are well-known models so the first reason is not a big problem. and we can take advantage of the second reason.

scholarly journals Forecast of Chaotic Series in a Horizon Superior to the Inverse of the Maximum Lyapunov Exponent

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Miguel Alfaro ◽  
Guillermo Fuertes ◽  
Manuel Vargas ◽  
Juan Sepúlveda ◽  
Matias Veloso-Poblete
Keyword(s):  
Lyapunov Exponent ◽  
Dynamic Systems ◽  
Chaotic Behavior ◽  
Chaotic Dynamic ◽  
Salt Lake ◽  
Global Dimension ◽  
Support Vector ◽  
Maximum Lyapunov Exponent ◽  
Forecast Models ◽  
Temporal Horizon

In this article, two models of the forecast of time series obtained from the chaotic dynamic systems are presented: the Lorenz system, the manufacture system, and the volume of the Great Salt Lake of Utah. The theory of the nonlinear dynamic systems indicates the capacity of making good-quality predictions of series coming from dynamic systems with chaotic behavior up to a temporal horizon determined by the inverse of the major Lyapunov exponent. The analysis of the Fourier power spectrum and the calculation of the maximum Lyapunov exponent allow confirming the origin of the series from a chaotic dynamic system. The delay time and the global dimension are employed as parameters in the models of forecast of artificial neuronal networks (ANN) and support vector machine (SVM). This research demonstrates how forecast models built with ANN and SVM have the capacity of making forecasts of good quality, in a superior temporal horizon at the determined interval by the inverse of the maximum Lyapunov exponent or theoretical forecast frontier before deteriorating exponentially.

scholarly journals Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

2002 ◽  
Vol 7 (1) ◽  
pp. 41-52 ◽  
Author(s):  
A. M. López Jiménez ◽  
C. Camacho Martínez Vara de Rey ◽  
A. R. García Torres
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Direct Methods ◽  
Short Time Series ◽  
Direct Estimation ◽  
Non Linear ◽  
Short Time

The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation ofλstarting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

scholarly journals Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Chuanfu Wang ◽  
Qun Ding
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Approximate Entropy ◽  
Chaotic Time Series ◽  
Pseudorandom Sequence ◽  
Periodic Behavior ◽  
Experimental Implementation ◽  
Sequence Generator

When chaotic systems are realized in digital circuits, their chaotic behavior will degenerate into short periodic behavior. Short periodic behavior brings hidden dangers to the application of digitized chaotic systems. In this paper, an approach based on the introduction of additional parameters to counteract the short periodic behavior of digitized chaotic time series is discussed. We analyze the ways that perturbation sources are introduced in parameters and variables and prove that the period of digitized chaotic time series generated by a digitized logistic map is improved efficiently. Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as a secure pseudorandom sequence generator for information encryption.

scholarly journals A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Equilibrium Analysis ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Topological Horseshoes

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

Dynamics, Analysis and Implementation of a Multiscroll Memristor-Based Chaotic Circuit

2016 ◽  
Vol 26 (08) ◽  
pp. 1650128 ◽  
Author(s):  
N. Henry Alombah ◽  
Hilaire Fotsin ◽  
E. B. Megam Ngouonkadi ◽  
Tekou Nguazon
Keyword(s):  
Chaotic Dynamics ◽  
Laboratory Experiments ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Hopf Bifurcations ◽  
Biometric Authentication ◽  
Chaotic Circuit ◽  
Circuit Element ◽  
Broadband Signal

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element — another inductor — is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication.

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