On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization

Mahmoud, Gamal M.; Ahmed, Mansour E.; Abed‐Elhameed, Tarek M.

doi:10.1016/j.ijleo.2016.10.095

Cited by 32 publications

(25 citation statements)

References 24 publications

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“…A bridge between the fractional‐order complex chaos and real hyperchaos was built in Liu by investigating complex modified hybrid projective synchronization. With respect to other recent representative works on this topic, we refer the reader to previous studies and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…However, in the aforementioned literature, authors do not consider chaos synchronization of multiple fractional‐order complex systems with ring connection as shown in Figure . In this chaotic model, the state variables of the first fractional‐order complex system couple the N th system, and the state variables of the second system couple the first, …analogically, until the state variables of the N th system couple those of the ( N −1)th.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

Jiang

Zhang

2018

Math Methods in App Sciences

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This paper is devoted to investigate synchronization and antisynchronization of N‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means of the direct design method, the appropriate controllers are designed to transform the fractional‐order error dynamical system into a nonlinear system with antisymmetric structure. Thus, by using the recently established result for the Caputo fractional derivative of a quadratic function and a fractional‐order extension of the Lyapunov direct method, several stability criteria are derived to ensure the occurrence of synchronization and antisynchronization among N‐coupled fractional‐order complex chaotic systems. Moreover, numerical simulations are performed to illustrate the effectiveness of the proposed design.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

Jiang

Zhang

2018

Math Methods in App Sciences

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“…In the meantime, lots of meritorious results on chaos synchronization of FOCCS have been reported, and various regimes of synchronization have been presented, such as complete synchronization (CS) [3,8,9], anti-synchronization (AS) [6,10], hybrid projective synchronization [11,12], combination synchronization [13,14], combination-combination synchronization [15], etc. For other recent works on this subject, please refer to the previous literature [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Xia

Jiang

2019

Entropy

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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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“…Compared to the normal projective synchronization scheme realized by one drive and one response system, combination projective synchronization has stronger anti-attack ability and antitranslated ability in secure communication. There are only a few papers on the combination projective synchronization [28,29]. On the other hand, the active control scheme [30][31][32] and backstepping design [33,34] have been widely recognized as two powerful design methods to control chaotic systems in recent years.…”

Section: Introductionmentioning

confidence: 99%

Active backstepping control of combined projective synchronization among different nonlinear systems

et al. 2017

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In this article, the authors have studied combination projective synchronization using active backstepping method. The main contribution of this effort is realization of the projective synchronization between two drive systems and one response system. We relax some limitations of previous work, where only combination complete synchronization has been investigated. According to Lyapunov stability theory and active backstepping design method, the corresponding controllers are designed to observe combination projective synchronization among three different classical chaotic systems, i.e. the Lorenz system, R€ ossler system and Chen system. The numerical simulation examples verify the effectiveness of the theoretical analysis. Combination projective synchronization has stronger anti-attack ability and antitranslated ability than the normal projective synchronization scheme realized by one drive and one response system in secure communication.

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On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization

Cited by 32 publications

References 24 publications

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Active backstepping control of combined projective synchronization among different nonlinear systems

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