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Volume 40 Number 3 Volume 40 Number 4 Volume 40 Number 5

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Research articles

ScienceAsia 40 (2014): 306-312 |doi: 10.2306/scienceasia1513-1874.2014.40.306

Mathematical models of nonlinear uniform consensus

Mansoor Saburova,*, Khikmat Saburovb

ABSTRACT:     We consider a nonlinear protocol for a structured time-invariant and synchronous multi-agent system. In the multi-agent system, we present opinion sharing dynamics as a trajectory of a cubic triple stochastic matrix. We provide a criterion for a uniform consensus of the multi-agent system. We show that the multi-agent system eventually reaches a consensus if either one of the following two conditions is satisfied: (i) every member of the group people has a positive subjective opinion on the given task after some revision steps or (ii) all entries of the given cubic triple stochastic matrix are positive.

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a Faculty of Science, International Islamic University Malaysia, 25200 Kuantan, Pahang, Malaysia
b University of West Bohemia, Pramenni 20/3 P.O.Box 301 00 Pilsen, Czech Republic

* Corresponding author, E-mail: msaburov@gmail.com

Received 11 Apr 2014, Accepted 25 Jul 2014