Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method

Srivastava, Mayank; Ansari, Sana Parveen; Agrawal, Saurabh; Das, S.; Leung, A.Y.T.

doi:10.1007/s11071-013-1177-0

Cited by 104 publications

(48 citation statements)

References 45 publications

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“…Lots of classical fractional-order real hyper-chaotic (chaotic) systems can be formed as system (7), such as the fractional-order real Chua system [7], the fractional-order real hyper-chaotic Rössler system [8], the fractional-order real Liu system [9] and other fractional-order real Lorenz-like systems [10]. Lots of classical fractional-order complex chaotic systems can be formed as system (8), such as fractional-order complex Lorenz system [15] and fractional-order complex Chen system [16].…”

Section: Mathematical Model and Problem Descriptionsmentioning

confidence: 99%

“…For example, Srivastava et al [10] studied anti-synchronization between identical and non-identical fractional-order chaotic systems using the active control method; Zhao and Wang [11] discussed global outer synchronization between two fractional-order complex networks coupled in a drive-response configuration; and Sun et al [12] investigated compound synchronization for four chaotic systems of integer order and fractional order. Projective synchronization (PS) has been especially extensively studied, because it can be used to obtain faster communication with its proportional feature, and the unpredictability of the scaling factor can additionally enhance the security of communication.…”

Section: Introductionmentioning

confidence: 99%

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Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

Liu

2014

Entropy

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This paper introduces a type of modified hybrid projective synchronization with complex transformation matrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformation matrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.

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Section: Mathematical Model and Problem Descriptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

Liu

2014

Entropy

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“…The most familiar synchronization phenomena are complete synchronization and anti-synchronized [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method

Aziz¹

2017

IJTAM

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This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti-synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu system as response system. Stabilization of error dynamics for each phenomenon is realized by satisfying Lyapunov's second method as a main tool. Theoretical analysis and numerical simulations are shown to verify the results.

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“…In fact, this necessary condition is not considered in the most of the existing works on anti-synchronization of chaotic systems (See for instance Refs. [8,9,10,11,12,13]). Moreover, the controllers obtained for achieving anti-synchronization of chaotic systems are structurally complex, i.e., some terms in those controllers are needed to counteract the redundant terms, such that E is not the equilibrium point of the error systemĖ = F(y) + F(x).…”

Section: Introductionmentioning

confidence: 99%

Coexistence of synchronization and anti-synchronization in chaotic systems

Ren

Guo

Vincent

2016

Archives of Control Sciences

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The coexistence of anti-synchronization and synchronization in chaotic systems is investigated. A novel algorithm is proposed to determine the variables of the master system that should anti-synchronize with corresponding variables of the slave system. Control strategies that guarantee the coexistence of synchronization and anti-synchronization in the unified chaotic system are presented; while numerical simulations are employed to validate and illustrate the effectiveness of the proposed method.

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Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method

Cited by 104 publications

References 45 publications

Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method

Coexistence of synchronization and anti-synchronization in chaotic systems

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