scholarly journals Adaptive full state hybrid function projective synchronization of financial hyperchaotic systems with uncertain parameters

2013 ◽  
Vol 18 (8) ◽  
pp. 2019-2028 ◽  
Author(s):  
Guoliang Cai ◽  
◽  
Lan Yao ◽  
Pei Hu ◽  
Xiulei Fang
Keyword(s):  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Full State ◽  
Hybrid Function ◽  
Hyperchaotic Systems

A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 351-359
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Abdulrahman Karouma ◽  
Salem Abdelmalek
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Projective Synchronization ◽  
The Novel ◽  
Fractional Order Systems ◽  
Function Projective Synchronization ◽  
Novel Approach ◽  
Full State ◽  
Hybrid Function ◽  
New Type

AbstractReferring to incommensurate fractional-order systems, this paper proposes a new type of chaos synchronization by combining full state hybrid function projective synchronization (FSHFPS) and inverse full state hybrid function projective synchronization (IFSHFPS). In particular, based on stability theory of linear integer-order systems and stability theory of linear fractional-order systems, the co-existence of FSHFPS and IFSHFPS between incommensurate fractional chaotic (hyperchaotic) systems is proved. To illustrate the capabilities of the novel approach proposed herein, numerical and simulation results are given.

THE HYBRID FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (05) ◽  
pp. 789-797
Author(s):  
YONG-GUANG YU ◽  
HAN-XIONG LI ◽  
JUN-ZHI YU
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Hybrid Function ◽  
Simulation Results ◽  
Different Chaotic Systems

This paper mainly investigated a hybrid function projective synchronization of two different chaotic systems. Based on the Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is designed. This technique is applied to achieve the synchronization between Lorenz and Rössler chaotic systems, and the synchronization of hyperchaotic Rössler and Chen systems. The numerical simulation results illustrate the effectiveness and feasibility of the proposed scheme.

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.

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