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We consider in this paper a discrete-time deterministic m-ary diffusion model over a strongly connected directed graph. The update rule is easy to state: let the vertices of the graph represent the agents and the edges represent the information flow; at every time step, each vertex updates its value to the maximum value held by its incoming neighbors at the last time step. The resulting system, defined...
The discrete-time Altafini model is an opinion dynamics model in which the interactions among a group of agents are described by a time-varying signed digraph. This paper first uses graph theoretic constructions to study modified versions of the Altafini model in which there are communication delays or quantized communication. The condition under which consensus in absolute value or bipartite consensus...
In a recent paper [1], a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting...
This paper considers the continuous-time Altafini model for opinion dynamics in which the interaction among a group of agents is described by a piecewise-constant switching signed digraph (or directed graph). Building on an idea proposed in [1], stability of the system described by the model is studied using a graphical approach. It is shown that for any sequence of repeatedly jointly strongly connected...
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