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International Conference on Difference Equations and Applications

ICDEA 2016: Advances in Difference Equations and Discrete Dynamical Systems pp 219–230Cite as

Reaching Consensus via Polynomial Stochastic Operators: A General Study

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 212)

Abstract

In this paper, we consider a nonlinear protocol for a structured time-varying synchronous multi-agent system in which an opinion sharing dynamics is presented by non-autonomous polynomial stochastic operators associated with high-order stochastic hyper-matrices. We show that the proposed nonlinear protocol generates the Krause mean process. We provide a criterion to establish a consensus in the multi-agent system under the proposed nonlinear protocol.

Keywords

  • Krause mean process
  • Markov chain with memory
  • Stochastic hyper-matrices
  • Polynomial stochastic operators
  • Consensus

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Acknowledgements

This work has been done under the MOHE grant FRGS14-141-0382. The first Author (M.S.) is grateful to the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. He is also indebted to Professor Hideaki Matsunaga for his kind hospitality during the conference ICDEA2016, Osaka, Japan.

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Authors and Affiliations

  1. Faculty of Science, International Islamic University Malaysia, 25200, Kuantan, Pahang, Malaysia

    Mansoor Saburov

  2. Mathematical Modeling Lab, MIMOS BERHAD, Technology Park Malaysia, 57000, Kuala Lumpur, Malaysia

    Khikmat Saburov

Authors
  1. Mansoor Saburov
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  2. Khikmat Saburov
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Corresponding author

Correspondence to Mansoor Saburov .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, Texas, USA

    Prof. Dr. Saber Elaydi

  2. Department of Information Science, Okayama University of Science, Okayama, Japan

    Prof. Dr. Yoshihiro Hamaya

  3. Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka, Japan

    Prof. Dr. Hideaki Matsunaga

  4. Institut für Mathematik, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Prof. Christian Pötzsche

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Saburov, M., Saburov, K. (2017). Reaching Consensus via Polynomial Stochastic Operators: A General Study. In: Elaydi, S., Hamaya, Y., Matsunaga, H., Pötzsche, C. (eds) Advances in Difference Equations and Discrete Dynamical Systems. ICDEA 2016. Springer Proceedings in Mathematics & Statistics, vol 212. Springer, Singapore. https://doi.org/10.1007/978-981-10-6409-8_14

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