Realization of a Novel Logarithmic Chaotic System and Its Characteristic Analysis

2019 ◽  
Vol 29 (02) ◽  
pp. 1930004 ◽  
Author(s):  
Xiaoyuan Wang ◽  
Xiaotao Min ◽  
Jun Yu ◽  
Yiran Shen ◽  
Guangyi Wang ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Nonlinear Term ◽  
Experimental Results ◽  
Characteristic Analysis ◽  
Chaotic Parameter ◽  
Hardware Circuit ◽  
Lyapunov Exponent Spectrum

To further improve the complexity of the chaotic system and broaden the chaotic parameter range, a novel logarithmic chaotic system was constructed by adding a nonlinear term of logarithm. The dynamic characteristics of the chaotic system were analyzed by chaotic phase diagram, bifurcation diagram, Lyapunov exponent spectrum, Poincaré mapping and dynamical map, etc. The system was digitized by DSP simulation, and the corresponding experimental results are completely consistent with the theoretical analysis. Furthermore, the equivalent hardware circuit was designed and theoretical analysis was verified by its experimental results.

HYPERCHAOS Qi SYSTEM

2010 ◽  
Vol 24 (24) ◽  
pp. 4771-4778 ◽  
Author(s):  
XING-YUAN WANG ◽  
YONG-FENG GAO ◽  
YAO-XIAN ZHANG
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Bifurcation Diagram ◽  
Nonlinear Term ◽  
Linear Term ◽  
Nonlinear Controller ◽  
Chaos System ◽  
Lyapunov Exponent Spectrum

This paper presents a four-dimensional hyperchaos Qi system, obtained by adding linear term and nonlinear term of nonlinear controller to Qi chaos system. The hyperchaos Qi system is studied by bifurcation diagram, Lyapunov exponent spectrum and phase diagram. Numerical simulations show that the new system's behavior can be periodic, chaotic and hyperchaotic as the parameter varies.

A New 3D Cubic Chaotic System and its Circuitry Implementation

2011 ◽  
Vol 130-134 ◽  
pp. 3924-3927
Author(s):  
Wei Deng ◽  
Yan Feng Wang ◽  
Jie Fang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Electronic Circuit ◽  
Nonlinear Term ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Lyapunov Dimension ◽  
New Chaotic System ◽  
Lyapunov Exponent Spectrum ◽  
New System

A new three-dimensional cubic chaotic system is reported. This new system contains five system parameters and each equation contains nonlinear term. Moreover, two equations of nonlinear term is cubic. The basic properties of the new system are investigated via theoretical analysis, numerical simulation, Lyapunov exponent spectrum, bifurcation diagram, Lyapunov dimension and Poincare diagram. The different dynamic behaviors of the new system are analyzed when each system parameter is changed .An electronic circuit was designed to realize the new chaotic system. Experimental chaotic behaviors of the system were found to be identical to the dynamic properties predicted by theoretical analysis and numerical simulations.

A Image Transmission System Based on Logistic Map

2012 ◽  
Vol 468-471 ◽  
pp. 727-732 ◽  
Author(s):  
Zhang Gang ◽  
Li Fang He ◽  
Tian Qi Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Communication System ◽  
Logistic Map ◽  
Image Transmission ◽  
Chaotic Synchronization ◽  
Synchronization System ◽  
Simulation Results ◽  
Chaotic Parameter ◽  
Lyapunov Exponent Spectrum

A method for chaotic synchronization system based on nonlinear control was studied. The general approach to chaotic system is following Logistic map. First, the parameter which meets chaotic status was analyzed and found via bifurcation diagram and Lyapunov exponent spectrum. The system can be synchronized quickly after just only a single iteration. Then, the method of implementing the synchronization system within a chaotic parameter modulation based communication system was researched. The deduction and simulation results also showed the probability for implementation the system in fast secure chaotic communications that require instant synchronization schemes. Finally, the chaotic system was applied in image transmission and the simulation results were also given.

Constructing Keyed Strong S-Box Using an Enhanced Quadratic Map

2021 ◽  
Vol 31 (10) ◽  
pp. 2150146
Author(s):  
Yuanyuan Si ◽  
Hongjun Liu ◽  
Yuehui Chen
Keyword(s):  
Phase Diagram ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Uniform Distribution ◽  
Bifurcation Diagram ◽  
Experimental Results ◽  
Kolmogorov Entropy ◽  
Symmetric Cryptography ◽  
Quadratic Map ◽  
Nonlinear Component

As the only nonlinear component for symmetric cryptography, S-Box plays an important role. An S-Box may be vulnerable because of the existence of fixed point, reverse fixed point or short iteration cycles. To construct a keyed strong S-Box, first, a 2D enhanced quadratic map (EQM) was constructed, and its dynamic behaviors were analyzed through phase diagram, Lyapunov exponent, Kolmogorov entropy, bifurcation diagram and randomness testing. The results demonstrated that the state points of EQM have uniform distribution, ergodicity and better randomness. Then a keyed strong S-Box construction algorithm was designed based on EQM, and the fixed point, reverse fixed point, and short cycles were eliminated. Experimental results verified the algorithm’s feasibility and effectiveness.

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

scholarly journals Hyperchaotic Circuit Based on Memristor Feedback with Multistability and Symmetries

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoyuan Wang ◽  
Xiaotao Min ◽  
Pengfei Zhou ◽  
Dongsheng Yu
Keyword(s):  
Theoretical Analysis ◽  
Dynamic Analysis ◽  
Chaotic System ◽  
Equilibrium Points ◽  
Experimental Results ◽  
System Dynamic ◽  
Hyperchaotic System ◽  
Analogue Circuits

A novel hyperchaotic circuit is proposed by introducing a memristor feedback in a simple Lorenz-like chaotic system. Dynamic analysis shows that it has infinite equilibrium points and multistability. Additionally, the symmetrical coexistent attractors are investigated. Further, the hyperchaotic system is implemented by analogue circuits. Corresponding experimental results are completely consistent with the theoretical analysis.

A New Fourth-Order Memristive Chaotic System and Its Generation

2015 ◽  
Vol 25 (11) ◽  
pp. 1550151 ◽  
Author(s):  
Yuxia Li ◽  
Xia Huang ◽  
Yiwen Song ◽  
Jinuan Lin
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Fourth Order ◽  
Bifurcation Analysis ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Diagram Analysis

In this paper, a new fourth-order memristive chaotic system is constructed on the basis of Chua's circuit. Chaotic behaviors are verified through a series of dynamical analyses, including Lyapunov exponent analysis, bifurcation analysis, and phase diagram analysis. In addition, chaos attractors in the newly-proposed system are implemented by hardware circuits.

Design of Grid Multiscroll Chaotic Attractors via Transformations

2015 ◽  
Vol 25 (10) ◽  
pp. 1530027 ◽  
Author(s):  
Xingxing Ai ◽  
Kehui Sun ◽  
Shaobo He ◽  
Huihai Wang
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Experimental Verification ◽  
Equilibrium Points ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
One Dimensional ◽  
Circular Grid

Three transformation approaches for generating grid multiscroll chaotic attractors are presented through theoretical analysis and numerical simulation. Three kinds of grid multiscroll chaotic attractors are generated based on one-dimensional multiscroll Chua system. The dynamics of the multiscroll chaotic attractors are analyzed by means of equilibrium points, eigenvalues, the largest Lyapunov exponent and complexity. As the experimental verification, we implemented the circular grid multiscroll attractor on DSP platform. The simulation and experimental results are consistent well with that of theoretical analysis, and it shows that the design approaches are effective.

Chaos in a Meminductor-Based Circuit

2016 ◽  
Vol 26 (08) ◽  
pp. 1650130 ◽  
Author(s):  
Fang Yuan ◽  
Guangyi Wang ◽  
Peipei Jin ◽  
Xiaoyuan Wang ◽  
Guojin Ma
Keyword(s):  
Lyapunov Exponent ◽  
Equivalent Circuit ◽  
Smooth Curve ◽  
Experimental Results ◽  
Chaotic Oscillator ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Equilibrium Set ◽  
Curve Model ◽  
Lyapunov Exponent Spectrum

A smooth curve model of meminductor and its equivalent circuit have been designed, on the condition that the meminductor is commonly unavailable. The equivalent circuit can be used for breadboard experiments for various application circuit designs of meminductor. Based on the meminductor, a new chaotic oscillator is proposed. The dynamical behaviors of the oscillator are investigated, including equilibrium set, Lyapunov exponent spectrum, bifurcations and dynamical map of the system. Particularly, the amplitude controlling is analyzed and coexisting attractors are found for conditions of different parameters. Furthermore, the experimental results are given to confirm the correction of the proposed meminductor model and the meminductor-based oscillator.

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