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We present two models of continuous opinion dynamics under bounded confidencewhich are representable as nonnegative discrete dynamical systems, namely theHegselmann-Krause model (Hegselmann and Krause, Journal of Artificial Societiesand Social Simulation 5(3), 2002) and the Deffuant-Weisbuch model (Deffuant etal, Advances in Complex Systems, 3, 2000). We fully characterize the set offixed points for both models. They are identical. Further on, we presentreformulations of both models on the more general level of densities of agentsin the opinion space as interactive Markov chains. We also characterize thesets of fixed points as identical in both models.

Fixed points in models of continuous opinion dynamics under bounded confidence