Some criteria for the global finite-time synchronization of two Lorenz–Stenflo systems coupled by a new controller

Chen, Yun; Shi, Zhangsong; Lin, Chunsheng

doi:10.1016/j.apm.2014.02.007

Cited by 14 publications

(12 citation statements)

References 29 publications

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“…Remark 2. Looking back to Theorem 1, it's easy to observe that the estimation of upper bound settling time (11) of FxS is independent of the initial states of chaotic systems…”

Section: Resultsmentioning

confidence: 99%

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Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

et al. 2022

Nonlinear Dyn

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This paper concerns the problem of fixed-time synchronization(FxS) of masterslave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand.Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

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“…Remark 2. Looking back to Theorem 1, it's easy to observe that the estimation of upper bound settling time (11) of FxS is independent of the initial states of chaotic systems…”

Section: Resultsmentioning

confidence: 99%

“…The sliding mode and adaptive techniques have been employed for guaranteeing the finite-time synchronization(FtS) between two distinct chaotic systems [10]. Chen et al have derived the sufficient conditions for achieving the global FtS between Lorenz-Stenflo systems [11].…”

Section: Introductionmentioning

confidence: 99%

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

et al. 2022

Nonlinear Dyn

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“…And we can get Boundedness of chaotic systems is an important concept in dynamical systems [24,25], which plays an important role in chaos control and chaos synchronization. Boundedness of the Lorenz system has been investigated by Leonov et al in a series of articles [26][27][28].…”

Section: Boundedness and Global Attractionmentioning

confidence: 99%

“…Despite the fact that many qualitative results on the Lorenz-Stenflo system have been obtained [19][20][21][22][23], there is a fundamental question that has not been completely answered so far: Is there a global trapping region for the Lorenz-Stenflo system? How to get the boundedness of a chaotic system is particularly significant both for theoretical research and engineering applications [13,24,29,30]. Motivated by the above discussion, we will investigate the ultimate bound set and the global attractive sets of the Lorenz-Stenflo system.…”

Section: Boundedness and Global Attractionmentioning

confidence: 99%

Complex Dynamical Behaviors of Lorenz-Stenflo Equations

Zhang

Xiao

2019

Mathematics

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A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

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“…For example, the finite-time synchronization of Lorenz systems has been early discussed by adopting the state feedback control [18]. Chen et al have studied the global finite-time synchronization between two chaotic Lorenz-Stenflo systems by employing the generalized variable substitution control [19]. For hyper-chaotic Lorenz system, the finite-time stability has been analyzed by designing adaptive control [20].…”

Section: Introductionmentioning

confidence: 99%

Predefined-time stabilization of Lorenz system with applications for stabilizing and synchronizing chaotic finance systems

Wu,

Gu,

et al. 2024

Phys. Scr.

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This article investigates the predefined-time stabilization (PtS) of the canonical Lorenz system at first, and then applies the derived results into the chaotic finance systems (CFSs) so as to realize the stabilization and synchronization, respectively. Compared with the traditional finite-/fixed-time stability analysis, the upper-bound of convergence time (UbCT) in this investigation can be set beforehand in need, which is an explicit constant regardless of initial values, system dimension, and controlling parameters. Moreover, the designed control schemes are non-chattering, which do not contain the conventional discontinuous signum and absolute value functions anymore. Via adopting the second Lyapunov method, the sufficient conditions are obtained successively for guaranteeing the realization of PtS for Lorenz system, CFS, as well as the predefined-time synchronization between two CFSs. The numerical experiments are finally arranged to manifest the correctness and effectiveness of the theoretical fruits, in which some comparison and perturbation analysis are made.

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Some criteria for the global finite-time synchronization of two Lorenz–Stenflo systems coupled by a new controller

Cited by 14 publications

References 29 publications

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

Complex Dynamical Behaviors of Lorenz-Stenflo Equations

Predefined-time stabilization of Lorenz system with applications for stabilizing and synchronizing chaotic finance systems

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