scholarly journals A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2593
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Yim-Fun Hu ◽  
Raed A. Abd-Alhameed ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Communication System ◽  
Secure Communication ◽  
Communication Systems ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Uncertain Parameter ◽  
Real World Applications

This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

A Chaotic System with Two Stable Equilibrium Points: Dynamics, Circuit Realization and Communication Application

2017 ◽  
Vol 27 (08) ◽  
pp. 1750130 ◽  
Author(s):  
Xiong Wang ◽  
Akif Akgul ◽  
Serdar Cicek ◽  
Viet-Thanh Pham ◽  
Duy Vo Hoang
Keyword(s):  
Chaotic System ◽  
Communication System ◽  
Secure Communication ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Circuit Realization ◽  
Shift Keying ◽  
Stable Equilibria ◽  
Chaos Shift Keying

Recent evidence suggests that a system with only stable equilibria can generate chaotic behavior. In this work, we study a chaotic system with two stable equilibrium points. The dynamics of the system is investigated via phase portrait, bifurcation diagram and Lyapunov exponents. The feasibility of the system is introducing its electronic realization. Moreover, the chaotic system is used in Symmetric Chaos Shift Keying (SCSK) and Chaotic ON-OFF Keying (COOK) modulated communication designs for secure communication. It is determined that the SCSK modulated communication system implemented with the chaotic system is more successful than COOK modulation for secure communication.

EXPANDED LORENZ SYSTEMS AND CHAOTIC SECURE COMMUNICATION SYSTEMS DESIGN

2006 ◽  
Vol 15 (04) ◽  
pp. 607-614 ◽  
Author(s):  
LEONARDO ACHO
Keyword(s):  
Communication System ◽  
Secure Communication ◽  
Communication Systems ◽  
Lorenz System ◽  
Systems Design ◽  
Lyapunov Theory ◽  
Globally Asymptotically Stable ◽  
Space Expansion ◽  
The Lorenz System ◽  
Chaotic Secure Communication

Using Lyapunov theory, the Lorenz chaotic system was partitioned in two parts, where one of them is globally asymptotically stable. This partition facilitated the state–space expansion of the Lorenz system from three to four-order. This new four-order Lorenz system, one of its states is synchronized with other. This expansion allows us to design a secure communication system where the dynamic of the receiver is just one-order. The proposed secure communication system uses two-lines of transmission. Simulation results are included to demonstrate the performance of this secure communication system based on this new four-order Lorenz system.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

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.

Bursting, Dynamics, and Circuit Implementation of a New Fractional-Order Chaotic System With Coexisting Hidden Attractors

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Meng Jiao Wang ◽  
Xiao Han Liao ◽  
Yong Deng ◽  
Zhi Jun Li ◽  
Yi Ceng Zeng ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Neuroendocrine Cells ◽  
Order System ◽  
Hidden Attractors ◽  
Main Mode ◽  
Circuit Realization

Systems with hidden attractors have been the hot research topic of recent years because of their striking features. Fractional-order systems with hidden attractors are newly introduced and barely investigated. In this paper, a new 4D fractional-order chaotic system with hidden attractors is proposed. The abundant and complex hidden dynamical behaviors are studied by nonlinear theory, numerical simulation, and circuit realization. As the main mode of electrical behavior in many neuroendocrine cells, bursting oscillations (BOs) exist in this system. This complicated phenomenon is seldom found in the chaotic systems, especially in the fractional-order chaotic systems without equilibrium points. With the view of practical application, the spectral entropy (SE) algorithm is chosen to estimate the complexity of this fractional-order system for selecting more appropriate parameters. Interestingly, there is a state variable correlated with offset boosting that can adjust the amplitude of the variable conveniently. In addition, the circuit of this fractional-order chaotic system is designed and verified by analog as well as hardware circuit. All the results are very consistent with those of numerical simulation.

Secure Communication based on a Fractional Order Chaotic System

2013 ◽  
Vol 7 (5) ◽  
pp. 205-216 ◽  
Author(s):  
Shuai Wang ◽  
Wei Sun ◽  
Cao-Yuan Ma ◽  
Di Wang ◽  
Zheng Chen
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication

SYNCHRONIZATION THEOREM FOR A CHAOTIC SYSTEM

1995 ◽  
Vol 05 (01) ◽  
pp. 297-302 ◽  
Author(s):  
JÖRG SCHWEIZER ◽  
MICHAEL PETER KENNEDY ◽  
MARTIN HASLER ◽  
HERVÉ DEDIEU
Keyword(s):  
Lyapunov Function ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Secure Communications ◽  
Error Feedback ◽  
Response System ◽  
Synchronization Method

Since Pecora & Carroll [Pecora & Carroll, 1991; Carroll & Pecora, 1991] have shown that it is possible to synchronize chaotic systems by means of a drive-response partition of the systems, various authors have proposed synchronization schemes and possible secure communications applications [Dedieu et al., 1993, Oppenheim et al., 1992]. In most cases synchronization is proven by numerically computing the conditional Lyapunov exponents of the response system. In this work a new synchronization method using error-feedback is developed, where synchronization is provable using a global Lyapunov function. Furthermore, it is shown how this scheme can be applied to secure communication systems.

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