Lag projective synchronization of fractional-order delayed chaotic systems

Zhang, Wei Wei; Cao, Jinde; Wu, Ranchao; Alsaadi, Fuad E.; Alsaedi, Ahmed

doi:10.1016/j.jfranklin.2018.10.024

Cited by 59 publications

(30 citation statements)

References 36 publications

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“…Meanwhile, several different types of synchronization for fractional-order chaotic systems have been observed and developed in the previous works. For instance, complete synchronization [13], phase synchronization [14], impulsive synchronization [15], and lag projective synchronization [16], just to enumerate a few examples.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

et al. 2019

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This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

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Section: Introductionmentioning

confidence: 99%

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

et al. 2019

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“…The chaotic systems studied in fractional calculus are numerous in literature. [19][20][21][22][23][24] A fractional chaotic model and its application to chaotic system have been discussed in the work of Atangana. 24 A fractional model with no-indexed law and its application to chaos and statistics have been considered in the work of Atangana and Go´mez-Aguilar.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

Khan

2019

Advances in Mechanical Engineering

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The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

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“…Especially, a chaotic system has the property that it is sensitive to the changing of initial conditions and the variations of the system parameters. Consequently, a large number of meritorious results on control and synchronization of fractional-order chaotic dynamics of nonlinear systems have become a hot research topic and a lot of interesting results have been reported, for example, in [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Robust Control of Disturbed Fractional‐Order Economical Chaotic Systems with Uncertain Parameters

Liu

et al. 2019

Complexity

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This paper focuses on the robust control of fractional-order economical chaotic system (FOECS) with parametric uncertainties and external disturbances. The dynamical behavior of FOECS is studied by numerical simulation, and circuit implementations of FOECS are also given. Based on fractional-order Lyapunov stability theorems, a robust adaptive controller, which can guarantee that all signals remain bounded and the tracking error tends to a small region, is designed. The proposed method can be used to control a large range of fractional-order systems with system uncertainties. Fractional-order adaptation laws are constructed to update the estimation of adaptive parameters. Finally, the robustness and effectiveness of our control method are indicated by simulation results.

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Lag projective synchronization of fractional-order delayed chaotic systems

Cited by 59 publications

References 36 publications

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

Robust Control of Disturbed Fractional‐Order Economical Chaotic Systems with Uncertain Parameters

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