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A discrete nonlinear and non-autonomous model of consensus formation. (English) Zbl 0988.39004

Elaydi, S. (ed.) et al., Communications in difference equations. Proceedings of the 4th international conference on difference equations, Poznan, Poland, August 27-31, 1998. Amsterdam: Gordon and Breach Science Publishers. 227-236 (2000).
Summary: Consensus formation among \(n\) experts is modeled as a positive discrete dynamical system in \(n\) dimensions. The well-known linear but non-autonomous model is extended to a nonlinear one admitting also various kinds of averaging besides the weighted arithmetic mean. For this model a sufficient condition for reaching a consensus is presented. As a special case consensus formation under bounded confidence is analyzed.
For the entire collection see [Zbl 0964.00041].

MSC:

39A11 Stability of difference equations (MSC2000)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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