Lag synchronization of hyperchaotic complex nonlinear systems

Mahmoud, Gamal M.; Mahmoud, Emad E.

doi:10.1007/s11071-011-0091-6

Cited by 96 publications

(63 citation statements)

References 34 publications

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“…The error between the real part of slave system x Re ( ) and the imaginary part of main system x Im ( − ) goes to zero as → ∞ (LS) [26].…”

Section: Remarkmentioning

confidence: 99%

“…As of late, a few sorts of synchronization with time lag were concentrated; for example, antilag synchronization (ALS), lag synchronization (LS), and modified projective lag synchronization (MPLS) of two riotous or hyperchaotic complex systems are investigated in [26][27][28][29]. In designing the applications, time delay always exists.…”

Section: Introductionmentioning

confidence: 99%

“…This is the speaker voice or transmitter at time − ( ≥ 0 and it is the lag time). In chaos communication, the time lag is the transmit flag that transmits to the receiver's end [26,27].…”

Section: Introductionmentioning

confidence: 99%

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A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Mahmoud

Abood

2017

Complexity

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Another chaotic nonlinear Lü model with complex factors is covered here. We can build this riotous complex system when we add a complex nonlinear term to the third condition of the complex Lü system and think of it as if every one of the factors is mind boggling or complex. This system in real adaptation is a 6-dimensional continuous autonomous chaotic system. Different types of chaotic complex Lü system are developed. Also, another sort of synchronization is presented by us which is simple for anybody to ponder for the chaotic complex nonlinear system. This sort might be called a complex antilag synchronization (CALS). There are irregular properties for CALS and they do not exist in the literature; for example, (i) the CALS contains or fused two sorts of synchronizations (antilag synchronization ALS and lag synchronization LS); (ii) in CALS the attractors of the main and slave systems are moving opposite or similar to each other with time lag; (iii) the state variable of the main system synchronizes with a different state variable of the slave system. A scheme is intended to accomplish CALS of chaotic complex systems in light of Lyapunov function. The acquired outcomes and effectiveness can be represented by a simulation case for our new model.

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“…The error between the real part of slave system x Re ( ) and the imaginary part of main system x Im ( − ) goes to zero as → ∞ (LS) [26].…”

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Mahmoud

Abood

2017

Complexity

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“…Some synchronous control methods have already been proposed for fractional-order chaotic systems [6], including the drive response method, sliding-mode control method, Lyapunov equation method, self-adaption control method, active control method, nonlinear feedback control method, and generalized synchronization method [7][8][9][10][11][12]. The sliding-mode adaptive robust control, for one, is not only characterized by quick responsiveness, excellent dynamic characteristics, robustness, and insensitiveness to external changes, but is able to control uncertainty in the system, among other attractive advantages.…”

Section: Introductionmentioning

confidence: 99%

Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Liu

Yang

2015

Entropy

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Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within the sliding-mode surface so as to realize synchronization of fractional-order chaotic systems. Analysis results demonstrate that the proposed single integral, sliding-mode control method can control the time delay fractional power system to realize chaotic synchronization, with strong robustness to external disturbance. The controller is simple in structure. The proposed method was also validated by numerical simulation.

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“…Recently, many complex dynamical systems have been proposed and studied [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The complex Lorenz equation is introduced in [9] and some of its dynamical properties are studied in [10].…”

Section: Introductionmentioning

confidence: 99%

Complex lag synchronization of two identical chaotic complex nonlinear systems

Mahmoud¹,

Abualnaja²

2014

Open Physics

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Abstract:Much progress has been made in the research of synchronization for chaotic real or complex nonlinear systems. In this paper we introduce a new type of synchronization which can be studied only for chaotic complex nonlinear systems. This type of synchronization may be called complex lag synchronization (CLS). A definition of CLS is introduced and investigated for two identical chaotic complex nonlinear systems. Based on Lyapunov function a scheme is designed to achieve CLS of chaotic attractors of these systems.

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Lag synchronization of hyperchaotic complex nonlinear systems

Cited by 96 publications

References 34 publications

A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Complex lag synchronization of two identical chaotic complex nonlinear systems

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