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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.
Acknowledgements
M. Saburov is grateful to the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. We are indeed greatly indebted to anonymous referees for their several helpful comments.
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Notes on contributors
M. Saburov
Mansoor Saburov received his BS and MS degrees in pure mathematics from the National University Uzbekistan in 2005 and 2007, respectively. He received his Ph.D. in pure mathematics from the International Islamic University Malaysia in 2011. He completed his post-doc in 2011–2012. Since 2012, he has been working as an assistant professor at the International Islamic University Malaysia. His research interests include nonlinear control, dynamical system, ergodic theory, and functional analysis.
K. Saburov
Khikmat Saburov received his BS degree in pure mathematics from the National University Uzbekistan in 2003. He received his MS and Ph.D. in Department of Mathematics, University of West Bohemia, Czech Republic, in 2006 and 2011, respectively. His research interests include graph theory, discrete mathematics, nonlinear control, and game theory.