Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems

Peng, Qiu; Jian, Jigui

doi:10.1016/j.chaos.2021.111072

Cited by 12 publications

(1 citation statement)

References 41 publications

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“…The calculation of the ultimate bound called Mittag-Leffler bound set for chaotic dynamical systems has been implemented for a small number of systems. The MLASs and MLPISs for the chaotic fractional systems have been estimated so far [32][33][34]. The main contribution of this research work is to estimate the MLASs and MLPISs for a fractional system that belongs to a special class of nonlinear systems with only cross-product nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

Liu

Muhsen²,

Shateyi

et al. 2023

Fractal Fract

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In this paper, the fractional-order chaotic system form of a four-dimensional system with cross-product nonlinearities is introduced. The stability of the equilibrium points of the system and then the feedback control design to achieve this goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, and the largest Lyapunov exponent are presented. Finally, the global Mittag–Leffler attractive sets (MLASs) and Mittag–Leffler positive invariant sets (MLPISs) of the considered fractional order system are presented. Numerical simulations are provided to show the effectiveness of the results.

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Section: Introductionmentioning

confidence: 99%

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

Liu

Muhsen²,

Shateyi

et al. 2023

Fractal Fract

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On the dynamical behaviors in fractional-order complex PMSM system and Hamilton energy control

Hou,

Lin,

Huang

et al. 2023

Nonlinear Dyn

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Chaos Control and Synchronization of a New Fractional Laser Chaotic System

Eshaghi,

Kadkhoda,

Inc

2024

Qual. Theory Dyn. Syst.

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In this article, we introduce a new fractional laser chaotic system derived from the Lorenz–Haken equations. We investigate the complex dynamics of the proposed system consisting chaos, stability, control and synchronization of chaos. Moreover, we numerically reveal the nonlinear dynamics of the fractional laser chaotic system through the phase portraits, time histories and bifurcation diagrams. Also, we indicate the chaotic behaviors of the system by means of Lyapunov exponents, bifurcation diagrams versus all parameters along the state variables, phase portraits and time histories with different trajectories and initial conditions. The necessary conditions to eliminate the chaotic vibration of the system are obtained via the feedback control procedure. Meanwhile, a synchronization mechanism based on the feedback control technique is achieved for coupled fractional laser chaotic systems. Furthermore, we show that the fractional derivative order is very effective on reducing the irregular and chaotic behaviors of the system.

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Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems

Cited by 12 publications

References 41 publications

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

Dynamical Behaviour, Control, and Boundedness of a Fractional-Order Chaotic System

On the dynamical behaviors in fractional-order complex PMSM system and Hamilton energy control

Chaos Control and Synchronization of a New Fractional Laser Chaotic System

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