Consensus of discrete-time opinion dynamics with stubbornness under fixed and switching topologies

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Abstract

We consider a discrete-time consensus dynamics of an opinion model with stubbornness under fixed and switching Topologies. Regarding the underlying network structures, both static and dynamically switching interaction topologies are considered. For the fixed topology, we prove that as long as the system parameters and initial states meet certain conditions, the presence of a rooted directed graph suffices for consensus. For the dynamically switching topology, under similar parametric conditions, consensus is guaranteed provided that the union of switched directed graphs over a bounded time interval contains a directed spanning tree. Numerical simulations are established to show the consensus and non-consensus phenomenon.

Keywords

discrete opinion model / consensus behavior / Rayleigh friction / static topology / dynamically switching topology

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