Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems

2001 ◽  
Vol 11 (3) ◽  
pp. 439-442 ◽  
Author(s):  
Daolin Xu ◽  
Zhigang Li ◽  
Steven R. Bishop
Keyword(s):  
Chaotic Systems ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization

Generalized Hybrid Dislocated Function Projective Synchronization of Chaotic Systems with Time Delay

2014 ◽  
Vol 574 ◽  
pp. 672-678 ◽  
Author(s):  
Rui Li ◽  
Guang Jun Zhang ◽  
Tao Zhu ◽  
Xu Jing Wang ◽  
Jun Dong
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In order to improve the security of secure communication, a novel generalized hybrid dislocated function projective synchronization (GHDFPS) was proposed and GHDFPS of time delay chaotic systems with uncertain parameters were researched in this paper. Due to time delay, the chaotic system can produce multiple positive Lyapunov exponential; this characteristic can enhance security in secure communications noticeably. Based on Lyapunove stability theory and modified hybrid feedback control method, the modified hybrid feedback controller and the parameter updating laws were designed for the GHDFPS between the two time delay chaotic systems with uncertain parameters. The feedback gain can be adjusted automatically according to the synchronization error values. Under the controller, generalized hybrid dislocated function projective synchronization of the two chaotic systems is achieved, and the uncertain parameters of response systems are identified. The chaotic item is added in the function scale factor. The chaotic item in the function scaling factor makes function scaling factor more complex and unpredictable. So this can enhance the features of indeterminism in secure communication. The time delay feedback Lorenz system as an example; by numerical simulations the effectiveness of the proposed method is demonstrated.

ROTATING SYNCHRONIZATION IN THREE-DIMENSIONAL CHAOTIC SYSTEMS

2012 ◽  
Vol 26 (20) ◽  
pp. 1250120 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Phase Space Reconstruction ◽  
Projective Synchronization ◽  
Reconstruction Method ◽  
Self Similarity ◽  
Application Fields ◽  
Three Dimensional Space

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other.

PROJECTIVE SYNCHRONIZATION OF UNIDENTICAL CHAOTIC SYSTEMS BASED ON STABILITY CRITERION

2006 ◽  
Vol 16 (04) ◽  
pp. 1049-1056 ◽  
Author(s):  
HONGJIE YU ◽  
JIANHUA PENG ◽  
YANZHU LIU
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
New Method ◽  
Projective Synchronization ◽  
Partially Linear ◽  
Higher Dimensional ◽  
The Lorenz System ◽  
The Stability

A new method of projective synchronization of unidentical chaotic systems is proposed in this letter. This method is based on the stability criterion of linear systems. The response of two unidentical chaotic systems can synchronize up to any desired scaling factor by a suitable separation of the systems. The new method of projective synchronization is suitable not only for the three-dimensional coupled partially linear systems, but also for higher dimensional even hyperchaotic systems. The simplicity and effectiveness of the proposed method are illustrated by the Lorenz system, the four-dimensional partially linear system, the four-dimensional hyperchaotic Rösser system and Chua's circuit system as four numerical examples.

scholarly journals CONTROLLED PROJECTIVE SYNCHRONIZATION IN NONPARTIALLY-LINEAR CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (06) ◽  
pp. 1395-1402 ◽  
Author(s):  
DAOLIN XU ◽  
ZHIGANG LI
Keyword(s):  
Linear Systems ◽  
Numerical Experiments ◽  
Chaotic Systems ◽  
Scaling Factor ◽  
The State ◽  
Projective Synchronization ◽  
High Dimensional ◽  
Hyperchaotic System ◽  
Partially Linear ◽  
Rossler System

Projective synchronization (PS), in which the state vectors synchronize up to a scaling factor, is usually observable only in partially linear systems. We show that PS could, by means of control, be extended to general classes of chaotic systems with nonpartial linearity. Performance of PS may also be manipulated by controlling the scaling factor to any desired value. In numerical experiments, we illustrate the applications to a Rössler system and a Chua's circuit. The feasibility of the control for high dimensional systems is demonstrated in a hyperchaotic system.

scholarly journals Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Babatunde Idowu ◽  
Kehinde Oyeleke ◽  
Cornelius Ogabi ◽  
Olasunkanmi Olusola
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Dimensional System

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

PROJECTIVE SYNCHRONIZATION OF A CLASS OF CHAOTIC SYSTEMS BASED ON OBSERVER

2011 ◽  
Vol 25 (28) ◽  
pp. 3765-3771 ◽  
Author(s):  
XING-YUAN WANG ◽  
XIN-GUANG LI
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Design Procedure ◽  
Scaling Factor ◽  
Observer Design ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Systematic Design ◽  
Unified Chaotic System ◽  
Placement Technique

Based on techniques from the state observer design and the pole placement technique, we present a systematic design procedure to synchronize a class of chaotic systems by a scaling factor (projective synchronization). Compared with the method proposed by Wen and Xu, this method eliminates the nonlinear item from the output of the drive system. Furthermore, the scaling factor can be adjusted arbitrarily in due course of control without degrading the controllability. Finally, feasibility of the technique is illustrated for the unified chaotic system.

Generalized Projective Synchronization for Fractional-Order Chaotic Systems with Different Fractional Order

2011 ◽  
Vol 474-476 ◽  
pp. 2106-2109 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Chen System ◽  
Response System ◽  
Generalized Projective Synchronization

In this paper, we propose a generalized projective synchronization with different scaling factor for fractional-order chaotic systems with different fractional order. A method of constructing response system is given. The generalized projective synchronization conditions are obtained theoretically. Finally, the fractional-order Chen system is used to demonstrate the effectiveness of the proposed schemes.

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