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 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.

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 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.

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.

A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM

2004 ◽  
Vol 14 (05) ◽  
pp. 1507-1537 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Constant Input ◽  
New Class ◽  
Dynamical Behaviors ◽  
Generalized Lorenz System ◽  
New Chaotic System

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-scroll chaotic attractor or confine two attractors to a 2-scroll chaotic attractor under the control of a simple constant input. Furthermore, the concept of generalized Lorenz system is extended to a new class of generalized Lorenz-like systems in a canonical form. Finally, the important problems of classification and normal form of three-dimensional quadratic autonomous chaotic systems are formulated and discussed.

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 Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Fei Yu ◽  
Li Liu ◽  
Shuai Qian ◽  
Lixiang Li ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Random Number Generator ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
The Novel ◽  
Multiple Attractors ◽  
Period 2 ◽  
Different Types ◽  
System Designs

Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.

scholarly journals Generation of Multi-Scroll Chaotic Attractors from a Jerk Circuit with a Special Form of a Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 842
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng
Keyword(s):  
Chaotic System ◽  
Special Form ◽  
Electronic Circuit ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
System Parameters ◽  
Left And Right

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.

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.

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