Phase synchronization in fractional differential chaotic systems

Erjaee, G.H.; Momani, Shaher

doi:10.1016/j.physleta.2007.11.065

Cited by 50 publications

(16 citation statements)

References 36 publications

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“…The asymptotic stability of phase synchronization, as one of the author proved in [57], is described in the following theorem. We recall that in the case of phase synchronization the error e(t) converges to or remains bounded by a constant c. Therefore, by just some modification on Theorem 1, we can analyze the convergence of phase synchronization.…”

Section: Stability Analysismentioning

confidence: 99%

Phase and anti-phase synchronization of fractional order chaotic systems via active control

Taghvafard

Erjaee

2011

Communications in Nonlinear Science and Numerical Simulation

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115

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Section: Stability Analysismentioning

confidence: 99%

Phase and anti-phase synchronization of fractional order chaotic systems via active control

Taghvafard

Erjaee

2011

Communications in Nonlinear Science and Numerical Simulation

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115

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“…The Mathieu-van der Pol hyperchaotic system [31][32][33] given by Figure 1 depicts the chaotic attractor of system (8). The phase portraits in x-y-z, y-z-w, x-z-w and x-y-w spaces are shown in figures 1a-1d, respectively.…”

Section: The Mathieu-van Der Pol Hyperchaotic Systemmentioning

confidence: 99%

Hyperchaos control and adaptive synchronization with uncertain parameter for fractional-order Mathieu–van der Pol systems

2015

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In this paper, we have discussed the local stability of the Mathieu-van der Pol hyperchaotic system with the fractional-order derivative. The fractional Routh-Hurwitz stability conditions were provided and were used to discuss the stability. Feedback control method was used to control chaos in the Mathieu-van der Pol system with fractional-order derivative and after controlling the chaotic behaviour of the system the synchronization between the fractional-order hyperchaotic Mathieu-van der Pol system and controlled system was introduced. In this study, modified adaptive control methods with uncertain parameters at various equilibrium points were used. Also the analysis of control time with respect to different fractional-order derivatives is the key feature of this paper. Numerical simulation results achieved using Adams-Boshforth-Moulton method show that the method is effective and reliable.

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“…Since the introduction of the synchronization for two chaotic signals starting at different initial conditions, more and more attention has been devoted to the control and synchronization for the chaotic and fractional‐order chaotic systems. Moreover, the types of synchronization are extended to complete synchronization, antisynchronization, phase synchronization, generalized synchronization, projective synchronization, and so on. In order to achieve these synchronizations, various synchronization methods such as linear and nonlinear feedback control, active control, adaptive control, sliding‐mode control, and backstepping design technique have been successfully used for the chaotic and fractional‐order chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional‐order hyperchaotic system

Chen

Lei

2018

Math Methods in App Sciences

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In this paper, for synchronizing two actual nonidentical fractional-order hyperchaotic systems disturbed by model uncertainty and external disturbance, the fractional matrix and inverse matrix projective synchronization methods are presented and the methods' correctness and effectiveness are proved. Especially, under certain degenerative conditions, the methods are reduced to study the complete synchronization, antisynchronization, projective (or inverse projective) synchronization, modified (or modified inverse) projective synchronization, and stabilization problem for the disturbed (or undisturbed) fractional-order hyperchaotic systems. In addition, as the fractional matrix and inverse matrix projective synchronization methods' applications, the fractional-order hyperchaotic Chen and Rabinovich systems disturbed by model uncertainty and external disturbance are constructed, and the matrix and inverse matrix projective synchronizations between the two disturbed systems are achieved, respectively. This work constructs a basic theoretical framework of fractional matrix and inverse matrix projective synchronization methods and provides a general method for synchronizing the actual disturbed fractional-order hyperchaotic systems that are related to science and engineering. KEYWORDS disturbed hyperchaotic system, fractional inverse matrix projective synchronization, fractional matrix projective synchronization, fractional-order derivative Math Meth Appl Sci. 2018;41:6907-6920.wileyonlinelibrary.com/journal/mma

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Phase synchronization in fractional differential chaotic systems

Cited by 50 publications

References 36 publications

Phase and anti-phase synchronization of fractional order chaotic systems via active control

Phase and anti-phase synchronization of fractional order chaotic systems via active control

Hyperchaos control and adaptive synchronization with uncertain parameter for fractional-order Mathieu–van der Pol systems

Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional‐order hyperchaotic system

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