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.

scholarly journals A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

scholarly journals Analyses and Encryption Implementation of a New Chaotic System Based on Semitensor Product

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Rui Wang ◽  
Peifeng Du ◽  
Wenqi Zhong ◽  
Han Han ◽  
Hui Sun
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
High Dimensions ◽  
New Chaotic System ◽  
Different Dimensions ◽  
Hardware Encryption ◽  
The Individual ◽  
New System ◽  
Randomness Tests

Semitensor product theory can deal with matrices multiplication with different numbers of columns and rows. Therefore, a new chaotic system for different high dimensions can be created by employing a semitensor product of chaotic systems with different dimensions, so that more channels can be selected for encryption. This paper proposes a new chaotic system generated by semitensor product applied on Qi and Lorenz systems. The corresponding dynamic characteristics of the new system are discussed in this paper to verify the existences of different attractors. The detailed algorithms are illustrated in this paper. The FPGA hardware encryption implementations are also elaborated and conducted. Correspondingly, the randomness tests are realized as well, and compared to that of the individual Qi system and Lorenz system, the proposed system in this paper owns the better randomness characteristic. The statistical analyses and differential and correlation analyses are also discussed.

A New Chaotic Attractor Around a Pre-Located Ring

2017 ◽  
Vol 27 (10) ◽  
pp. 1750152 ◽  
Author(s):  
Zhen Wang ◽  
Zhe Xu ◽  
Ezzedine Mliki ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Specific Property ◽  
Unique Property ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
New Chaotic Attractor ◽  
New System

Designing chaotic systems with specific features is a very interesting topic in nonlinear dynamics. However most of the efforts in this area are about features in the structure of the equations, while there is less attention to features in the topology of strange attractors. In this paper, we introduce a new chaotic system with unique property. It has been designed in such a way that a specific property has been injected to it. This new system is analyzed carefully and its real circuit implementation is presented.

scholarly journals A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

2018 ◽  
Vol 8 (6) ◽  
pp. 4951 ◽  
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Mustafa Mamat ◽  
Muhammad Afendee Mohamed ◽  
Mada Sanjaya WS
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Equilibrium Curve ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.

scholarly journals A Novel Fast Convergence Control Scheme for a Class of 3D Chaotic Systems with Uncertain Parameters and External Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Haipeng Su ◽  
Runzi Luo ◽  
Ling Xu ◽  
Meichun Huang ◽  
Jiaojiao Fu
Keyword(s):  
Lyapunov Function ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Fast Convergence ◽  
Uncertain Parameters ◽  
External Disturbances ◽  
Solution Approach ◽  
New Chaotic System ◽  
Convergence Control ◽  
The Stability

This paper studies the control of a class of 3D chaotic systems with uncertain parameters and external disturbances. A new method which is referred as the analytical solution approach is firstly proposed for constructing Lyapunov function. Then, for suppressing the trajectories of the 3D chaotic system to its equilibrium point 00,0,0, a novel fast convergence controller containing parameter λ which determines the convergence rate of the system is presented. By using the designed Lyapunov function, the stability of the closed-loop system is proved via the Lyapunov stability theorem. Computer simulations are employed to a new chaotic system to illustrate the effectiveness of the theoretical results.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2507-2521 ◽  
Author(s):  
C. SARASOLA ◽  
A. D'ANJOU ◽  
F. J. TORREALDEA ◽  
A. MOUJAHID
Keyword(s):  
Phase Space ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Chaotic Systems ◽  
Quantitative Measure ◽  
Energy Functions ◽  
Dissipation Of Energy ◽  
Rossler System ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

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.

Evolutionary Algorithm Based Solution of Rössler Chaotic System Using Bernstein Polynomials

2020 ◽  
Vol 17 (7) ◽  
pp. 2932-2939
Author(s):  
Rania A. Alharbey ◽  
Kiran Sultan
Keyword(s):  
Chaotic System ◽  
Fitness Function ◽  
Bernstein Polynomials ◽  
Three Dimensional ◽  
Accurate Estimation ◽  
Interior Point Algorithm ◽  
Research Attention ◽  
Rossler System ◽  
Rössler System ◽  
Error Dynamics

Chaotic systems have gained enormous research attention since the pioneering work of Lorenz. Rössler system stands among the extensively studied classical chaotic models. This paper proposes a technique based on Bernstein Polynomial Basis Function to convert the three-dimensional Rössler system of Ordinary Differential Equations (ODEs) into an error minimization problem. First, the properties of Bernstein Polynomials are applied to derive the fitness function of Rössler chaotic system. Second, in order to obtain the values of unknown Bernstein coefficients to optimize the fitness function, the problem is solved using two versatile algorithms from the family of Evolutionary Algorithms (EAs), Genetic Algorithm (GA) hybridized with Interior Point Algorithm (IPA) and Differential Algorithm (DE). For validity of the proposed technique, simulation results are provided which verify the global stability of error dynamics and provide accurate estimation of the desired parameters.

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