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Reaching a consensus: a discrete nonlinear time-varying case

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  • M. Saburov
  • K. Saburov

Abstract

In this paper, we have considered a nonlinear protocol for a structured time-varying and synchronous multi-agent system. By means of cubic triple stochastic matrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of a non-homogeneous system of cubic triple stochastic matrices. We show that the multi-agent system eventually reaches to a consensus if either of the following two conditions is satisfied: (1) every member of the group people has a positive subjective distribution on the given task after some revision steps or (2) all entries of some cubic triple stochastic matrix are positive.

Suggested Citation

  • M. Saburov & K. Saburov, 2016. "Reaching a consensus: a discrete nonlinear time-varying case," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2449-2457, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:10:p:2449-2457
    DOI: 10.1080/00207721.2014.998743
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    1. Wang, Qingyun & Duan, Zhisheng & Chen, Guanrong & Feng, Zhaosheng, 2008. "Synchronization in a class of weighted complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5616-5622.
    2. Farrukh Mukhamedov & Mansoor Saburov & Izzat Qaralleh, 2013. "On -Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, November.
    3. Peng, Ke & Yang, Yupu, 2009. "Leader-following consensus problem with a varying-velocity leader and time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 193-208.
    4. Galam, Serge, 2004. "Contrarian deterministic effects on opinion dynamics: “the hung elections scenario”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 453-460.
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