A study of the dynamic of influence through differential equations.

*(English)*Zbl 1248.91086The paper proposes a continuous dynamical model of influence in which agents make their decisions on a certain issue. The model takes into account the opportunity of the agents to change their initial decision, under some possible influences from other agents in the network. This change of opinion can take place on an iterative manner. The agents could also assign weights to each issue, reflecting the importance given to them. These importance weights could be either positive, negative or zero, corresponding to the stimulation of the agent by the others, the inhibition, or the absence of any relation between the two agents in question. The weighted sum of the opinions that a certain agent receives from of all the other agents defines the exhortation obtained by the agent. The dynamics of the model is represented by a system of ODEs, in which the variables are the inclinations of the agents. The authors have shown that if the majority function is used, then the decision of each agent converges to the inclination of the guru. They also describe necessary and sufficient conditions for an agent to be follower of a coalition, and for a set to be the boss set or the approval set of an agent.

Reviewer: Iulian Stoleriu (Iaşi)

##### MSC:

91D30 | Social networks; opinion dynamics |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

37N40 | Dynamical systems in optimization and economics |

35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |

##### Keywords:

social network; inclination; importance weight; decision; influence function; differential equations
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\textit{E. Maruani} et al., RAIRO, Oper. Res. 46, No. 1, 83--106 (2012; Zbl 1248.91086)

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