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On the Fractional Continuous-Time Hegselmann–Krause’s Type Consensus Model

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

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Abstract

The consensus problem of fractional-order multi-agent continuous-time systems is considered. In the system, interactions between opinions are defined like in Hegselmann–Krause models but with included memory by fractional-order operator on the left side of nonlinear system. In the paper we investigate various models for the dynamics of fractional order opinions by analytical methods as well as by computer simulations.

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References

  1. Blondel, V.D., Hendrickx, J.M., Tsitsiklis, F.N.: Continuous-time average- preserving opinion dynamics with opinion-dependent communications. SIAM J. Control Optim. 48(8), 5214–5240 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence models, analysis, and simulations. J. Artif. Soc. Soc. Simul. 5(3), 227–236 (2002)

    Google Scholar 

  3. Krause, U.: A discrete nonlinear and non-autonomous model of consensus formation. Proc. Commun. Differ. Equ. pp. 227–236 (2000)

    Google Scholar 

  4. Mozyrska, D., Wyrwas, M.: Fractional discrete-time of Hegselmann–Krause’s type consensus model with numerical simulations. Submitted into Neurocomputing (2016)

    Google Scholar 

  5. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North–Holland Mathematics Studies, 204. Elsevier Science B. V., Amsterdam (2006)

    Google Scholar 

  6. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  7. Blondel, V.D., Hendrickx, J.M., Tsitsiklis, F.N.: On Krause’s multi-agent consensus model with state-dependent connectivity. IEEE Trans. Automat. Contr. 5(11), 2586–2597 (2009)

    Article  MathSciNet  Google Scholar 

  8. Li, Y., Chen, Y.Q., Podlubny, I.: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica 45, 1965–1969 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Mozyrska, D., Girejko, E., Wyrwas, M.: Fractional nonlinear systems with sequential operators. Cent. Eur. J. Phys. 11(10), 1295–1303 (2013)

    MATH  Google Scholar 

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Acknowledgments

The work was supported by Polish founds of National Science Center, granted on the basis of decision DEC-2014/15/B/ST7/05270.

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Authors and Affiliations

  1. Bialystok University of Technology, Wiejska 45A, 15-351, Białystok, Poland

    Ewa Girejko, Dorota Mozyrska & Małgorzata Wyrwas

Authors
  1. Ewa Girejko
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  2. Dorota Mozyrska
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  3. Małgorzata Wyrwas
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Corresponding author

Correspondence to Ewa Girejko .

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Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Girejko, E., Mozyrska, D., Wyrwas, M. (2017). On the Fractional Continuous-Time Hegselmann–Krause’s Type Consensus Model. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_3

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

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