Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control

Chen, Diyi; Zhang, Runfan; Sprott, J. C.; Chen, Haitao; Ma, Xiaoyi

doi:10.1063/1.4721996

Cited by 71 publications

(36 citation statements)

References 40 publications

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“…In order to achieve behavior of the add order synchronization between two different dimensional fractional order chaotic systems with fully unknown parameters, we take the fractional-order hyperchaotic Chen system [35] to be the master system and the fractional-order chaotic Chen system [11] to be the slave system. The variables of the master system are represented by subscript 1 and the slave system by subscript 2.…”

Section: Modified Adaptive Add Order Synchronization Of Two Differentmentioning

confidence: 99%

Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters

Al-Sawalha¹,

Ghazel²,

Ababneh³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, an adaptive control scheme is developed to study the add order synchronization and the add order antisynchronization behavior between two different dimensional fractional order chaotic systems with fully uncertain parameters. This design of adaptive controller is based on the Lyapunov stability theory. Analytic expression for the controller with its adaptive laws of parameters is shown. The adaptive add order synchronization and add order anti-synchronization between two fractional order chaotic systems are used to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are used to verify the results.

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Section: Modified Adaptive Add Order Synchronization Of Two Differentmentioning

confidence: 99%

Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters

Al-Sawalha¹,

Ghazel²,

Ababneh³

et al. 2017

J. Nonlinear Sci. Appl.

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“…2, like in Section 2, we can see that the three coupled Rössler chaotic systems realize synchronization in a short amount of time, so the above generic criteria of global chaos synchronization is effective. 4 The secure communication theory and multistage chaos synchronized system for secure communications…”

Section: Proofmentioning

confidence: 99%

“…In recent years, the idea of synchronization of chaotic systems has received a great deal of interest among scientists from various fields [1][2][3][4][5][6][7][8]. In their seminal paper, Pecora and Carroll addressed the synchronization of chaotic system by using a drive-response configuration.…”

Section: Introductionmentioning

confidence: 99%

Adaptive coupled synchronization among three coupled chaos systems and its application to secure communications

Zhang

Zhang²,

et al. 2016

J Wireless Com Network

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In this paper, the adaptive synchronization method of three coupled identical chaos systems is proposed. New generic criteria of global chaos synchronization and strict theoretical proofs are given. The unidirectional (bidirectional) coupled system will synchronize by adding three adaptive feedback gain equations. As an example, the three Rössler chaotic systems with unidirectional coupling are given to realize the adaptive coupled synchronization; at the same time, the three Lorenz chaotic systems donate the bidirectional coupling adaptive synchronization. This paper also extends the above adaptive synchronization method to secure chaos communications through the method of chaos masking. Based on the three coupled identical Lorenz chaotic systems, a novel method of chaos encryption is proposed, and the basic idea is that after encrypting two times in two transmitters and one receiver, information signal can be recovered exactly at the receiver end. In consideration of interfering random white noise, the results of encoding and decoding are simulated and analyzed for the multistage chaos synchronized system. By analyzing the characteristics of noise, this paper presents a de-noising method using wavelet transform. At last, a secure communications method for high amplitude information signal transmission based on chaotic masking is studied. With the MATLAB, the effects of signal de-noising could be demonstrated.

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“…People have applied it to control chaos because it can drive the state which is not on the sliding surface to the steady state in limited time [25,26]. However, there are almost no relevant outcomes about sliding mode control for general class of 4-D fractional-order chaos.…”

Section: Introductionmentioning

confidence: 99%

Simplified Sliding Mode of a Novel Class of Four-dimensional Fractional-order Chaos

Wang¹,

Li²,

Zhu³

2015

IJCA

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Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control

Cited by 71 publications

References 40 publications

Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters

Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters

Adaptive coupled synchronization among three coupled chaos systems and its application to secure communications

Simplified Sliding Mode of a Novel Class of Four-dimensional Fractional-order Chaos

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