A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

2007 ◽  
Vol 16 (11) ◽  
pp. 3238-3243 ◽  
Author(s):  
Wang Fan-Zhen ◽  
Chen Zeng-Qiang ◽  
Wu Wen-Juan ◽  
Yuan Zhu-Zhi
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Lorenz Chaotic System

scholarly journals Hybrid Image Encryption Technique Using Genetic Algorithm and Lorenz Chaotic System

2020 ◽  
Vol 32 ◽  
pp. 03009
Author(s):  
Vishwanath Chikkareddi ◽  
Anurag Ghosh ◽  
Preksha Jagtap ◽  
Sahil Joshi ◽  
Jeel Kanzaria
Keyword(s):  
Genetic Algorithm ◽  
Image Encryption ◽  
Chaotic System ◽  
Random Number ◽  
Current Image ◽  
Space Efficiency ◽  
Highly Sensitive ◽  
Key Sensitivity ◽  
Lorenz Chaotic System ◽  
Time And Space Complexity

One of the important application of image encryption is storing confidential and important images on a local device or a database in such a way that only the authorized party can view or perceive it. The current image encryption technique employs the genetic algorithm to increase confusion in the image, but compromises in time and space complexity. The other method employs chaos or pseudo random number generating systems which have fast and highly sensitive keys but fails to make the image sufficiently noisy and is risky due to its deterministic nature. We propose a technique which employs the non-deterministic, optimizing power of genetic algorithm and the space efficiency and key sensitivity of chaotic systems into a unified, efficient algorithm which will retain the merits of both the methods whereas tries to minimize their demerits in a software system. The encryption process proceeds in two steps, generating two keys. First, an encryption sequence is generated using Lorenz Chaotic system of differential equation. The seed values used are the user’s actual key having key sensitivity of 10-14. Second, the encrypted image’s genetic encryption sequence is generated which will result in an encrypted image with entropy value greater than 7.999 thus ensuring the image is very noisy. Proposed technique uses variations of Lorenz system seed sets to generate all random mutations and candidate solutions in Genetic encryption. Since only the seed sets leading to desired solution is stored, space efficiency is higher compared to storing the entire sequences. Using this image encryption technique we will ensure that the images are hidden securely under two layers of security, one chaotic and other non-deterministic.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

scholarly journals Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jiezhi Wang ◽  
Qing Zhang ◽  
Zengqiang Chen ◽  
Hang Li
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Three Dimensional ◽  
Boundary Region ◽  
Cross Product ◽  
State Equation ◽  
Linear Coefficient ◽  
Analytical Expression ◽  
Product Term ◽  
Cross Product Term

Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of theith state variable in theith state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in each equation. A numerical solution and an analytical expression of the ultimate bounds are received. To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved. The corresponding ultimate boundary regions are demonstrated through numerical simulations. Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization. Numerical simulation exhibits the feasibility of the designed scheme.

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

scholarly journals Multiple-Image Encryption Algorithm Based on the 3D Permutation Model and Chaotic System

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 660 ◽  
Author(s):  
Xiaoqiang Zhang ◽  
Xuesong Wang
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Three Dimensional ◽  
Multiple Image ◽  
External Mode ◽  
Large Numbers ◽  
Permutation Model ◽  
Magic Cube ◽  
Exclusive Or ◽  
Image Encryption Algorithm

Large numbers of images are produced in many fields every day. The content security of digital images becomes an important issue for scientists and engineers. Inspired by the magic cube game, a three-dimensional (3D) permutation model is established to permute images, which includes three permutation modes, i.e., internal-row mode, internal-column mode, and external mode. To protect the image content on the Internet, a novel multiple-image encryption symmetric algorithm (block cipher) with the 3D permutation model and the chaotic system is proposed. First, the chaotic sequences and chaotic images are generated by chaotic systems. Second, the sender permutes the plain images by the 3D permutation model. Lastly, the sender performs the exclusive OR operation on permuted images. The simulation and algorithm comparisons display that the proposed algorithm possesses desirable encryption images, high security, and efficiency.

scholarly journals A novel three-dimensional autonomous chaotic system

2011 ◽  
Vol 60 (3) ◽  
pp. 030503
Author(s):  
Feng Chao-Wen ◽  
Cai Li ◽  
Kang Qiang ◽  
Zhang Li-Sen
Keyword(s):  
Chaotic System ◽  
Three Dimensional

A NEW CHAOTIC SYSTEM AND ITS GENERATION

2003 ◽  
Vol 13 (01) ◽  
pp. 261-267 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamical Behaviors ◽  
New Chaotic System

This Letter introduces a relatively simple three-dimensional continuous autonomous chaotic system, which can display complex 2- and 4-scroll attractors in simulations. Its generation and basic dynamical behaviors are briefly described.

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