Rössler-network with time delay: Univariate impulse pinning synchronization

Kun Tian; Hai Peng Ren; Celso Grebogi

doi:10.1063/5.0017295

Rössler-network with time delay: Univariate impulse pinning synchronization

Kun Tian, Hai Peng Ren^* (Corresponding Author), Celso Grebogi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Rössler had a brilliant and successful life as a scientist during which he published a benchmark dynamical system by using an electronic circuit interpreting chemical reactions. This is our contribution to honor his splendid erudite career. It is a hot topic to regulate a network behavior using the pinning control with respect to a small set of nodes in the network. Besides pinning to a small number of nodes, small perturbation to the node dynamics is also demanded. In this paper, the pinning synchronization of a coupled Rössler-network with time delay using univariate impulse control is investigated. Using the Lyapunov theory, a theorem is proved for the asymptotic stability of synchronization in the network. Simulation is given to validate the correctness of the analysis and the effectiveness of the proposed univariate impulse pinning controller.

Original language	English
Article number	123101
Number of pages	12
Journal	Chaos
Volume	30
Issue number	12
Early online date	1 Dec 2020
DOIs	https://doi.org/10.1063/5.0017295
Publication status	Published - Dec 2020

Keywords

R¨ossler-Network with time delay
univariate impulse control
pinning strategy
synchronization theorem

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Tian_et_al_Chaos_RosslerNetworkWithTime_AAM
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science 30:12 and may be found at https://doi.org/10.1063/5.0017295
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Tian_et_al_Chaos_RosslerNetworkWithTime_VoR
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science 30:12 and may be found at https://doi.org/10.1063/5.0017295
Final published version, 3.16 MBLicence: Unspecified

Cite this

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title = "R{\"o}ssler-network with time delay: Univariate impulse pinning synchronization",

abstract = "R{\"o}ssler had a brilliant and successful life as a scientist during which he published a benchmark dynamical system by using an electronic circuit interpreting chemical reactions. This is our contribution to honor his splendid erudite career. It is a hot topic to regulate a network behavior using the pinning control with respect to a small set of nodes in the network. Besides pinning to a small number of nodes, small perturbation to the node dynamics is also demanded. In this paper, the pinning synchronization of a coupled R{\"o}ssler-network with time delay using univariate impulse control is investigated. Using the Lyapunov theory, a theorem is proved for the asymptotic stability of synchronization in the network. Simulation is given to validate the correctness of the analysis and the effectiveness of the proposed univariate impulse pinning controller.",

keywords = "R¨ossler-Network with time delay, univariate impulse control, pinning strategy, synchronization theorem",

author = "Kun Tian and Ren, {Hai Peng} and Celso Grebogi",

note = "ACKNOWLEDGMENTS: This paper was supported in part by the Shaanxi Provincial Special Support Program for Science and Technology Innovation Leader. ",

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T2 - Univariate impulse pinning synchronization

AU - Tian, Kun

AU - Ren, Hai Peng

AU - Grebogi, Celso

N1 - ACKNOWLEDGMENTS: This paper was supported in part by the Shaanxi Provincial Special Support Program for Science and Technology Innovation Leader.

PY - 2020/12

Y1 - 2020/12

N2 - Rössler had a brilliant and successful life as a scientist during which he published a benchmark dynamical system by using an electronic circuit interpreting chemical reactions. This is our contribution to honor his splendid erudite career. It is a hot topic to regulate a network behavior using the pinning control with respect to a small set of nodes in the network. Besides pinning to a small number of nodes, small perturbation to the node dynamics is also demanded. In this paper, the pinning synchronization of a coupled Rössler-network with time delay using univariate impulse control is investigated. Using the Lyapunov theory, a theorem is proved for the asymptotic stability of synchronization in the network. Simulation is given to validate the correctness of the analysis and the effectiveness of the proposed univariate impulse pinning controller.

AB - Rössler had a brilliant and successful life as a scientist during which he published a benchmark dynamical system by using an electronic circuit interpreting chemical reactions. This is our contribution to honor his splendid erudite career. It is a hot topic to regulate a network behavior using the pinning control with respect to a small set of nodes in the network. Besides pinning to a small number of nodes, small perturbation to the node dynamics is also demanded. In this paper, the pinning synchronization of a coupled Rössler-network with time delay using univariate impulse control is investigated. Using the Lyapunov theory, a theorem is proved for the asymptotic stability of synchronization in the network. Simulation is given to validate the correctness of the analysis and the effectiveness of the proposed univariate impulse pinning controller.

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KW - synchronization theorem

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Rössler-network with time delay: Univariate impulse pinning synchronization

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Keywords

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