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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Mathematical Models of Nonlinear Uniform Consensus II

Journal of Applied Nonlinear Dynamics 7(1) (2018) 95--104 | DOI:10.5890/JAND.2018.03.008

Mansoor Saburov, Khikmat Saburov

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

College of Engineering and Technology, American University of the Middle East, 54200, Egaila, Kuwait

Mathematical Modeling Laboratory, MIMOS Berhad, 57000 Kuala Lumpur, Malaysia

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This paper is a continuation of our previous studies on nonlinear consensus. We have considered a nonlinear protocol for a structured time-invariant and synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of a polynomial stochastic operator associated with a stochastic multidimensional hyper-matrix. We provide a criterion for a uniform consensus in the multi-agent system. Particularly, the uniform consensus is achieved in the multi-agent system if all entries of the stochastic multidimensional hyper-matrix are positive. Some numerical results are also presented to support our theoretical results.


This work has been done under the MOHE grant FRGS14-141-0382. The Author (M.S.) is grateful to the Junior Associate scheme of the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.


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