Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems

Wen, Guilin; Xu, Daolin

doi:10.1016/j.chaos.2004.09.117

Cited by 144 publications

(51 citation statements)

References 19 publications

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“…In order to achieve the modified projective synchronization, the controller u for the active control [15,20,21] is chosen to obtaiṅ…”

Section: Creation Of Hopf Limit Circles Based On Mpsmentioning

confidence: 99%

“…The robustness of the created limit circle can be well guaranteed in advance because the responses of the original dynamical system are directly synchronized with the existing Hopf limit circle of the drive system. Moreover, the amplitudes of the created limit circle can be arbitrarily diminished or enlarged by manipulating the scaling factors of MPS [14][15][16]. With the aid of the appropriate controller, the MPS between two nonidentical systems can be achieved and the center point of the created Hopf limit circle may be translated into any proper location required in real application.…”

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confidence: 99%

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Designing Hopf limit circle to dynamical systems via modified projective synchronization

Wen

2010

Nonlinear Dyn

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In order to affirmatively utilize the characteristics of Hopf limit circle, a control method to design Hopf circle with proper characteristics into dynamical system is established based on the modified projective synchronization (MPS). The proposed method may serve as a complete solution to design a stable Hopf limit circle, which can simultaneously achieve the following three properties: with the desired amplitudes and shape changes, with the pre-specified location center, and at a pre-specified system parameter location. In contrast to the methods based on Hopf bifurcation theory, the new method is independent of the verbose procedures for the bifurcation critical conditions and the stability analysis. Numerical examples demonstrate the effectiveness of the proposed method.

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“…In order to achieve the modified projective synchronization, the controller u for the active control [15,20,21] is chosen to obtaiṅ…”

Section: Creation Of Hopf Limit Circles Based On Mpsmentioning

confidence: 99%

mentioning

confidence: 99%

Designing Hopf limit circle to dynamical systems via modified projective synchronization

Wen

2010

Nonlinear Dyn

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“…In applications to secure communications, this feature can be used to extend binary digital to M-nary digital communication [6] for achieving fast communication. Projective synchronization of identical chaotic systems has been extremely investigated in recent years, including finite dimensional systems [4,[7][8][9], infinite dimensional systems [10][11][12], and complex networks [13,14]. But in practical situations, it is hardly the case that every component can be assumed to be identical.…”

Section: Introductionmentioning

confidence: 99%

Projective synchronization between two different time-delayed chaotic systems using active control approach

Feng

2010

Nonlinear Dyn

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In this paper, we investigate the projective synchronization between two different time-delayed chaotic systems. A suitable controller is chosen using the active control approach. We relax some limitations of previous work, where projective synchronization of different chaotic systems can be achieved only in finite dimensional chaotic systems, so we can achieve projective synchronization of different chaotic systems in infinite dimensional chaotic systems. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective synchronization between two different time-delayed chaotic systems. The validity of the proposed method is demonstrated and verified by observing the projective synchronization between two well-known time-delayed chaotic systems; the Ikeda system and Mackey-Glass system. Numerical simulations fully support the analytical approach.

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“…Mainieri and Rehacek [9] first proposed the chaos projective synchronization scheme in 1999, but it was still very difficult to achieve projective synchronization between two or more chaotic nonlinear systems until Wen et al [10,11] presented an observer-based control scheme for projective chaos synchronization in 2004, whose prominent advantage is "no special limitation" for nonlinear dynamical systems to achieve projective chaos synchronization. Wen and co-authors also tried to explore the potential applications of projective synchronization to noise reduction in mechanical engineering [12,13], design bifurcation solutions [14,15] and so on.…”

Section: Introductionmentioning

confidence: 99%

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Xin

2015

Entropy

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A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.

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Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems

Cited by 144 publications

References 19 publications

Designing Hopf limit circle to dynamical systems via modified projective synchronization

Designing Hopf limit circle to dynamical systems via modified projective synchronization

Projective synchronization between two different time-delayed chaotic systems using active control approach

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

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