Dual projective synchronization between integer-order and fractional-order chaotic systems

Optik ◽  
2017 ◽  
Vol 141 ◽  
pp. 90-98 ◽  
Author(s):  
Qing Zhang ◽  
Jian Xiao ◽  
Xiao-Qing Zhang ◽  
Duan-yang Cao
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Integer Order

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

Fuzzy Adaptive Controller for Synchronization of Uncertain Fractional-Order Chaotic Systems

2018 ◽  
pp. 190-217 ◽  
Author(s):  
Amel Bouzeriba
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
External Disturbances ◽  
Fuzzy Approximation ◽  
Adaptive Laws ◽  
Adaptive Fuzzy Logic ◽  
Fuzzy Adaptive Controller ◽  
Fuzzy Adaptive

In this chapter, the projective synchronization problem of different multivariable fractional-order chaotic systems with both uncertain dynamics and external disturbances is studied. More specifically, a fuzzy adaptive controller is investigated for achieving a projective synchronization of uncertain fractional-order chaotic systems. The adaptive fuzzy-logic system is used to online estimate the uncertain nonlinear functions. The latter is augmented by a robust control term to efficiently compensate for the unavoidable fuzzy approximation errors, external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is employed to derive the parameter adaptation laws and to prove the boundedness of all signals of the closed-loop system. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

scholarly journals Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 481 ◽  
Author(s):  
Zhonghui Li ◽  
Tongshui Xia ◽  
Cuimei Jiang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Order Complex ◽  
Order Error ◽  
New Type ◽  
Modified Projective Synchronization ◽  
The Stability ◽  
Complex Chaotic Systems

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

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