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.

Some New Dissipative Chaotic Systems with Cyclic Symmetry

2018 ◽  
Vol 28 (13) ◽  
pp. 1850164 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Shirin Panahi ◽  
Anitha Karthikeyan ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Cyclic Symmetry ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Basin Of Attraction

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited. Finally, the circuit implementation is carried out to show their feasibility.

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.

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 A New Memristor-Based 5D Chaotic System and Circuit Implementation

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Rui Wang ◽  
Mingjin Li ◽  
Zhaoling Gao ◽  
Hui Sun
Keyword(s):  
Chaotic System ◽  
Adaptive Synchronization ◽  
Dynamics Analysis ◽  
Slave System ◽  
Circuit Implementation ◽  
Physical Experiments ◽  
New Chaotic System ◽  
New System

This paper proposes a new 5D chaotic system with the flux-controlled memristor. The dynamics analysis of the new system can also demonstrate the hyperchaotic characteristics. The design and analysis of adaptive synchronization for the new memristor-based chaotic system and its slave system are carried out. Furthermore, the modularized circuit designs method is used in the new chaotic system circuit implementation. The Multisim simulation and the physical experiments are conducted, compared, and matched with each other which can demonstrate the existence of the attractor for the new system.

A GENERALIZED 3-D FOUR-WING CHAOTIC SYSTEM

2009 ◽  
Vol 19 (11) ◽  
pp. 3841-3853 ◽  
Author(s):  
ZENGHUI WANG ◽  
GUOYUAN QI ◽  
YANXIA SUN ◽  
MICHAËL ANTONIE VAN WYK ◽  
BAREND JACOBUS VAN WYK
Keyword(s):  
Phase Diagrams ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Bifurcation Diagrams ◽  
Basic Properties ◽  
New System

In this paper, several three-dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have similar features. A simpler and generalized 3-D continuous autonomous system is proposed based on these features which can be extended to existing 3-D four-wing chaotic systems by adding some linear and/or quadratic terms. The new system can generate a four-wing chaotic attractor with simple topological structures. Some basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincaré maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

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.

Design and Impelemation of Two Switchable Chaotic Systems

2011 ◽  
Vol 217-218 ◽  
pp. 1725-1728
Author(s):  
Wei Fan ◽  
Zhong Lin Wang ◽  
Ming Qing Xu ◽  
Ai Feng Wang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Lyapunov Dimension ◽  
New Chaotic System

A new chaotic system is built which is consists of two subsystems. A subsystem is analyzed such as equilibrium, eigenvalue, Lyapunov, dimension and Lyapunov exponent. A practical circuit is designed to realize the system and the experimentation is carried out. The manifold chaotic attractor of the two subsystems is observed in the oscillograph, it is good agree with simulation.

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 Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 958 ◽  
Author(s):  
Alaa Kadhim Farhan ◽  
Nadia M.G. Al-Saidi ◽  
Abeer Tariq Maolood ◽  
Fahimeh Nazarimehr ◽  
Iqtadar Hussain
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Unique Feature ◽  
Engineering Application ◽  
New Chaotic System ◽  
Entropy Measurement ◽  
Reliable Performance ◽  
Encryption Method

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

CAN A THREE-DIMENSIONAL SMOOTH AUTONOMOUS QUADRATIC CHAOTIC SYSTEM GENERATE A SINGLE FOUR-SCROLL ATTRACTOR?

2004 ◽  
Vol 14 (04) ◽  
pp. 1395-1403 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Phase Space ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
System Parameters ◽  
New Chaotic System

Recently, we have investigated a new chaotic system of three-dimensional autonomous quadratic ordinary differential equations, and found that the system visually displays a four-scroll chaotic attractor confirmed by both numerical simulations and circuit implementation. In this paper, we further study the following question: Is it really true that this system can generate a four-scroll chaotic attractor, or is it only a numerical artifact? By a more careful theoretical analysis along with some further numerical simulations, we conclude that the four-scroll chaotic attractor of this system, which we observed on both computer and oscilloscope, cannot actually exist in theory. The fact is that this system has two co-existing two-scroll chaotic attractors that are arbitrarily close in the phase space for some system parameters, therefore extremely tiny numerical round-off errors or signal fluctuations will nudge the system orbit to switch from one attractor to another, thereby forming the seemingly single four-scroll chaotic attractor on screen display.

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