BRIDGE BETWEEN THE HYPERCHAOTIC LORENZ SYSTEM AND THE HYPERCHAOTIC CHEN SYSTEM

2011 ◽  
Vol 25 (05) ◽  
pp. 711-721 ◽  
Author(s):  
CHAO MA ◽  
XINGYUAN WANG
Keyword(s):  
Bifurcation Analysis ◽  
System Parameter ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Lyapunov Dimension ◽  
Dual Systems ◽  
Chen System ◽  
New Findings ◽  
Hyperchaotic Lorenz System ◽  
New System

This paper presents a novel unified hyperchaotic system that contains the hyperchaotic Lorenz system and the hyperchaotic Chen system as two dual systems at the two extremes of its parameter spectrum. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic Lorenz system to the hyperchaotic Chen system. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension.

BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM

2002 ◽  
Vol 12 (12) ◽  
pp. 2917-2926 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG ◽  
SERGEJ CELIKOVSKY
Keyword(s):  
Chaotic System ◽  
System Parameter ◽  
Lorenz System ◽  
Dual Systems ◽  
Chen System ◽  
Entire Spectrum ◽  
Unified Chaotic System ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
New System

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

scholarly journals Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yi Chai ◽  
Liping Chen ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Hyperchaotic Systems

This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.

GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (30) ◽  
pp. 1350195 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU ◽  
CHAO LUO
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Pole Placement ◽  
Generalized Synchronization ◽  
Chen System ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme.

A Novel Approach for Designing Dynamical S-Boxes Using Hyperchaotic System

2012 ◽  
Vol 6 (1) ◽  
pp. 100-119 ◽  
Author(s):  
Jun Peng ◽  
Du Zhang ◽  
Xiaofeng Liao
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Hyperchaotic System ◽  
Differential Approximation ◽  
Novel Approach ◽  
Substitution Boxes ◽  
Hyperchaotic Lorenz System ◽  
Digital Image Encryption ◽  
Image Encryption Algorithm ◽  
Independence Criterion

In the information security field, the substitution boxes (S-boxes) have been extensively used in many cryptographic systems. This paper presents a novel approach for generating dynamically cryptographically S-boxes using a four-dimensional hyperchaotic Lorenz system. Within the algorithm, the initial condition is employed to drive the hyper-chaotic system to generate a chaotic sequence which is used to construct a chaotic key-dependent S-box. With different system initial conditions, many of distinct S-boxes can be obtained dynamically. Some cryptographic properties for a good S-box such as bijection, nonlinearity, SAC (Strict Avalanche Criterion), BIC (Bit Independence Criterion), and differential approximation probability are found to hold in the obtained S-boxes. The analytic results indicated that all the criteria for designing strong S-boxes can be achieved. The comparison of the proposed method for generating S-boxes with other chaos-based schemes indicates that our S-boxes have a better performance with respect to some properties. Finally, the authors give an example of a digital image encryption algorithm using their S-box and the results of image statistical analysis show that the algorithm has the desirable cryptographic properties.

Generalized Projective Synchronization of Diverse Structures Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 568-570 ◽  
pp. 1095-1099
Author(s):  
Si Yan Tao ◽  
Da Lin ◽  
Xiao Hui Zeng
Keyword(s):  
General Class ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems

In this paper, the generalized projective synchronization for a general class of hyperchaotic systems is investigated. A systematic, powerful and concrete scheme is developed to investigate the generalized projective synchronization between the drive system and response system based on the feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes.

scholarly journals Synchronization of Coupled Nonidentical Fractional-Order Hyperchaotic Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zhouchao Wei
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Chen System ◽  
Mode Method ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaotic Systems

Synchronization of coupled nonidentical fractional-order hyperchaotic systems is addressed by the active sliding mode method. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. Furthermore, synchronizing fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system is performed to show the effectiveness of the proposed controller.

GENERALIZED (LAG, ANTICIPATED AND COMPLETE) PROJECTIVE SYNCHRONIZATION IN TWO NONIDENTICAL CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2012 ◽  
Vol 26 (16) ◽  
pp. 1250121
Author(s):  
XINGYUAN WANG ◽  
LULU WANG ◽  
DA LIN
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.

scholarly journals A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Taiyong Li ◽  
Minggao Yang ◽  
Jiang Wu ◽  
Xin Jing
Keyword(s):  
Image Encryption ◽  
Fractional Order ◽  
Dna Computing ◽  
Lorenz System ◽  
Effective Diffusion ◽  
Encryption Algorithm ◽  
Pseudorandom Sequence ◽  
Hyperchaotic System ◽  
Diffusion Scheme ◽  
Hyperchaotic Lorenz System

In the era of the Internet, image encryption plays an important role in information security. Chaotic systems and DNA operations have been proven to be powerful for image encryption. To further enhance the security of image, in this paper, we propose a novel algorithm that combines the fractional-order hyperchaotic Lorenz system and DNA computing (FOHCLDNA) for image encryption. Specifically, the algorithm consists of four parts: firstly, we use a fractional-order hyperchaotic Lorenz system to generate a pseudorandom sequence that will be utilized during the whole encryption process; secondly, a simple but effective diffusion scheme is performed to spread the little change in one pixel to all the other pixels; thirdly, the plain image is encoded by DNA rules and corresponding DNA operations are performed; finally, global permutation and 2D and 3D permutation are performed on pixels, bits, and acid bases. The extensive experimental results on eight publicly available testing images demonstrate that the encryption algorithm can achieve state-of-the-art performance in terms of security and robustness when compared with some existing methods, showing that the FOHCLDNA is promising for image encryption.

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