scholarly journals Coexisting infinitely many attractors in a new chaotic system with a curve of equilibria: Its extreme multi-stability and Kolmogorov–Sinai entropy computation

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988804
Author(s):  
Atefeh Ahmadi ◽  
Xiong Wang ◽  
Fahimeh Nazarimehr ◽  
Fawaz E Alsaadi ◽  
Fuad E Alsaadi ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Phase Portraits ◽  
Initial Condition ◽  
Bifurcation Diagrams ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
The Mathematical Model

A new five-dimensional chaotic system with extreme multi-stability is introduced in this article. The mathematical model is established, and numerical simulations are done. This dynamical system complicates incident of extreme multi-stability. Most significantly, relied on the mathematical model, the recently proposed system has a curve of equilibria that ends in the occurrence of hidden attractors. We examine the initial-condition-dependent dynamics of this system. We inspect that there is an unrestricted number of coexistent attractors, which signifies the occurrence of extreme multi-stability strictly. In addition, the extreme multi-stability according to initial condition is investigated consuming the Lyapunov exponent spectra and bifurcation diagrams. The existence of coexisting infinitely many attractors is displayed with phase portraits. In the end, we calculate and debate Kolmogorov–Sinai entropy in the chaotic system. We direct trying the Kolmogorov–Sinai technique of entropic inspection for the dynamics of the system.

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 Simple Chaotic Flow with Hyperbolic Sinusoidal Function and Its Application to Voice Encryption

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2047
Author(s):  
Saleh Mobayen ◽  
Christos Volos ◽  
Ünal Çavuşoğlu ◽  
Sezgin S. Kaçar
Keyword(s):  
Chaotic System ◽  
Random Number ◽  
Random Number Generator ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
Chaotic Flows ◽  
Chaotic Flow ◽  
New Chaotic System ◽  
Sinusoidal Function

In this article, a new chaotic system with hyperbolic sinusoidal function is introduced. This chaotic system provides a new category of chaotic flows which gives better perception of chaotic attractors. In the proposed chaotic flow with hyperbolic sinusoidal function, according to the changes of parameters of the system, the self-excited attractor and two forms of hidden attractors are occurred. Dynamic behavior of the offered chaotic flow is studied through eigenvalues, bifurcation diagrams, phase portraits, and spectrum of Lyapunov exponents. Moreover, the existence of double-scroll attractors in real word is considered via the Orcard-PSpice software through an electronic execution of the new chaotic flow and illustrative results between the numerical simulation and Orcard-PSpice outcomes are obtained. Lastly, random number generator (RNG) design is completed with the new chaos. Using the new RNG design, a novel voice encryption algorithm is suggested and voice encryption use and encryption analysis are performed.

A Novel Four-Dimensional No-Equilibrium Hyper-Chaotic System With Grid Multiwing Hyper-Chaotic Hidden Attractors

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Sen Zhang ◽  
Yi Cheng Zeng ◽  
Zhi Jun Li
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Control Technique ◽  
Nonlinear Functions ◽  
Hidden Attractors ◽  
Remarkable Feature

By using a simple state feedback control technique and introducing two new nonlinear functions into a modified Sprott B system, a novel four-dimensional (4D) no-equilibrium hyper-chaotic system with grid multiwing hyper-chaotic hidden attractors is proposed in this paper. One remarkable feature of the new presented system is that it has no equilibrium points and therefore, Shil'nikov theorem is not suitable to demonstrate the existence of chaos for lacking of hetero-clinic or homo-clinic trajectory. But grid multiwing hyper-chaotic hidden attractors can be obtained from this new system. The complex hidden dynamic behaviors of this system are analyzed by phase portraits, the time domain waveform, Lyapunov exponent spectra, and the Kaplan–York dimension. In particular, the Lyapunov exponent spectra are investigated in detail. Interestingly, when changing the newly introduced nonlinear functions of the new hyper-chaotic system, the number of wings increases. And with the number of wings increasing, the region of the hyper-chaos is getting larger, which proves that this novel proposed hyper-chaotic system has very rich and complicated hidden dynamic properties. Furthermore, a corresponding improved module-based electronic circuit is designed and simulated via multisim software. Finally, the obtained experimental results are presented, which are in agreement with the numerical simulations of the same system on the matlab platform.

A New 4D Chaotic System with Coexisting Hidden Chaotic Attractors

2020 ◽  
Vol 30 (10) ◽  
pp. 2050142
Author(s):  
Lihua Gong ◽  
Rouqing Wu ◽  
Nanrun Zhou
Keyword(s):  
Chaotic System ◽  
Dynamic Characteristics ◽  
Dynamic Properties ◽  
Random Number Generator ◽  
Phase Portraits ◽  
Hidden Attractors ◽  
System A ◽  
Offset Boosting ◽  
New Chaotic System ◽  
Linear State

A new 4D chaotic system with infinitely many equilibria is proposed using a linear state feedback controller in the Sprott C system. Although the new 4D chaotic system has only two nonlinear terms, it has rich dynamic characteristics, such as hidden attractors and coexisting attractors. Besides, the freedom of offset boosting of a variable is achieved by adjusting a controlled constant. The dynamic characteristics of the new chaotic system are fully analyzed from the aspects of phase portraits, bifurcation diagrams, Lyapunov exponents and Poincaré maps. The corresponding analogue electronic circuit is designed and implemented to verify the new 4D chaotic system. By taking advantage of the complex dynamic properties of the new chaotic system, a random number generator algorithm is proposed.

DCSK performance analysis of a chaos-based communication using a newly designed chaotic system

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Namrata Biswas ◽  
Raja Mohamed I
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Signal ◽  
Coherent Detection ◽  
Phase Portraits ◽  
Modulation Scheme ◽  
Threshold Control ◽  
New Chaotic System ◽  
Shift Keying ◽  
Chaos Shift Keying

Abstract In this paper, a new chaotic system has been introduced and the fundamental properties of the system were investigated and presented using a bifurcation diagram, max Lyapunov exponent (LE) and phase portraits. The synchronization of the drive and response system has been done using the threshold control parameter. Later the differential chaos shift keying (DCSK) modulation scheme has been carried out for the system as it is the most efficient modulation scheme. The demodulator detects the data without the use of chaotic signal phase recovery, as it uses the non-coherent detection technique. The results were compared with other modulation schemes using the bit error rate (BER) graph. It reveals that the proposed chaos-based system could be used for secure communication. The system has been implemented using the MATLAB Simulink technique.

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.

Generating Multiple Chaotic Attractors from Sprott B System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650177 ◽  
Author(s):  
Qiang Lai ◽  
Shiming Chen
Keyword(s):  
Lyapunov Exponent ◽  
Function Method ◽  
Polynomial Function ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Phenomenon ◽  
Bifurcation Diagrams ◽  
Initial Values ◽  
Index 2 ◽  
Lyapunov Exponent Spectrum

Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear phenomenon, but there are few studies that have previously addressed it to our best knowledge. In this paper, we propose a polynomial function method for generating multiple chaotic attractors from the Sprott B system. The polynomial function extends the number of index-2 saddle foci, which determines the emergence of multiple chaotic attractors in the system. The analysis of the equilibria is presented. Two coexisting chaotic attractors, three coexisting chaotic attractors and four coexisting chaotic attractors are investigated for verifying the effectiveness of the method. The chaotic characteristics of the attractors are shown by bifurcation diagrams, Lyapunov exponent spectrum and phase portraits.

THE GENERATION AND ANALYSIS OF A NEW FOUR-DIMENSIONAL HYPERCHAOTIC SYSTEM

2007 ◽  
Vol 18 (06) ◽  
pp. 1013-1024 ◽  
Author(s):  
JIEZHI WANG ◽  
ZENGQIANG CHEN ◽  
ZHUZHI YUAN
Keyword(s):  
Lyapunov Exponent ◽  
Cross Product ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Bifurcation Diagrams ◽  
Dynamic Behaviors ◽  
System Parameters ◽  
Product Term ◽  
Two Parameters ◽  
Cross Product Term

A new four-dimensional continuous autonomous hyperchaotic system is considered. It possesses two parameters, and each equation of it has one quadratic cross product term. Some basic properties of it are studied. The dynamic behaviors of it are analyzed by the Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits, and Poincaré sections. The system has larger hyperchaotic region. When it is hyperchaotic, the two positive LE are both large and they are both larger than 1 if the system parameters are taken appropriately.

scholarly journals A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design

2019 ◽  
Vol 9 (4) ◽  
pp. 2336 ◽  
Author(s):  
Aceng Sambas ◽  
Mustafa Mamat ◽  
Ayman Ali Arafa ◽  
Gamal M Mahmoud ◽  
Mohamad Afendee Mohamed ◽  
...  
Keyword(s):  
Circuit Design ◽  
Chaotic System ◽  
Passive Control ◽  
Electronic Circuit ◽  
Control Method ◽  
Phase Portraits ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
Line Of Equilibria ◽  
Line Equilibrium

<p>A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the  new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study.</p>

scholarly journals A Novel Voltage-Controlled Tri-Valued Memristor and Its Application in Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Xiaoyuan Wang ◽  
Xue Zhang ◽  
Meng Gao
Keyword(s):  
Mathematical Model ◽  
Nonlinear Systems ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Chaotic Systems ◽  
Nonlinear Element ◽  
Nonlinear Characteristics ◽  
Nanometer Size ◽  
New Chaotic System

Memristor is a kind of passive nonlinear element, which is widely used in nonlinear systems, especially chaotic systems, because of its nanometer size, nonvolatile property, and good nonlinear characteristics. Compared with general chaotic systems, chaotic systems based on memristors have richer dynamic characteristics. However, the current research mainly focuses on the binary and continuous chaotic systems based on memristors, and studies on the tri-valued and multi-valued memristor chaotic systems are relative scarce. For this reason, a mathematical model of tri-valued memristor is proposed, and the circuit characteristics of the model are studied. Furthermore, based on this model, a new chaotic system is designed and analyzed. This innovation enriches the types of chaotic systems and lays the foundation for the application of tri-valued and multi-valued memristors in nonlinear systems.

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