Adaptive Modified Projective Synchronization Between Genesio and Rossler Chaotic Systems with Uncertainties

2012 ◽  
Vol 546-547 ◽  
pp. 1040-1044 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Ji Fei Liu ◽  
Rui Pan
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Projective Synchronization ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Control Laws ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Modified Projective Synchronization ◽  
Different Chaotic Systems

The paper discusses the modified projective synchronization of two different chaotic systems by nonlinear control laws, considering the conditions of the master-slave systems with uncertain parameters, the synchronization problem between Genesio system and Rossler system has been investigated, adopting the adaptive control method, a sufficient condition is attainted for the modified projective synchronization between master and slave system, finally, The control performances are verified by the numerical examples.

scholarly journals Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

2017 ◽  
Vol 7 (6) ◽  
pp. 3436
Author(s):  
Hamed Tirandaz ◽  
Mohsen Ahmadnia ◽  
Hamid Reza Tavakoli
Keyword(s):  
Nonlinear Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Adaptive Methods ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Synchronization Problem ◽  
Modified Projective Synchronization ◽  
Nonlinear Control Method ◽  
Speed And Accuracy

<p>The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views.</p>

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.

PROJECTIVE SYNCHRONIZATION OF DIFFERENT CHAOTIC SYSTEMS WITH NONLINEARITY INPUTS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250059 ◽  
Author(s):  
YUJUN NIU ◽  
XINGYUAN WANG
Keyword(s):  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
External Noise ◽  
Projective Synchronization ◽  
Adaptive Technique ◽  
Noise Disturbances ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
The Given

In this paper, projective synchronization of different chaotic systems is studied, in the presence of uncertainties of system parameter variation, external noise disturbance and nonlinearity inputs. Using adaptive technique, sliding mode control method and pole assignment technique, an adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor, without requiring the bounds of the system uncertainties and external noise disturbances be known in advance. The results of numerical simulation further verify the effectiveness and feasibility of the proposed scheme.

scholarly journals A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Wang ◽  
Bin Zhen ◽  
Jian Xu
Keyword(s):  
System Approach ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Necessary And Sufficient Condition ◽  
Simple Analysis ◽  
Projective System ◽  
New Approach ◽  
Modified Projective Synchronization ◽  
Different Chaotic Systems ◽  
Necessary And Sufficient

A new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to judge the occurrence of modified projective synchronization. Theoretical analysis and numerical simulations show that, although the projective system may not be unique, modified projective synchronization can be achieved provided that the origin of any of projective systems is asymptotically stable. Furthermore, an example is presented to illustrate that even a necessary and sufficient condition for modified projective synchronization can be derived by using the projective system approach.

Function Projective Synchronization between two Different Chaotic Systems

2007 ◽  
Vol 62 (1-2) ◽  
pp. 29-33 ◽  
Author(s):  
Yong Chen ◽  
Xin Li
Keyword(s):  
Chaotic Systems ◽  
Projective Synchronization ◽  
Complete Synchronization ◽  
Function Projective Synchronization ◽  
Unified Chaotic System ◽  
Control Scheme ◽  
Modified Projective Synchronization ◽  
Set Up ◽  
Different Chaotic Systems ◽  
Function Matrix

A function projective synchronization is defined to synchronize two different systems up to a scaling function matrix f with different initial values. The function projective synchronization is more general than the complete synchronization, the generalized projective synchronization and the modified projective synchronization. The corresponding framework of synchronization is set up and used to achieve a function projective synchronization design of two different chaotic systems: the unified chaotic system and the Rössler system. Feasibility of the proposed control scheme is illustrated through the numerical simulation.

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