A Continuous Opinions Discrete Actions Model on Line Graphs

Francesca Ceragioli (), Paolo Frasca () and Raoul Prisant ()
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Francesca Ceragioli: Politecnico di Torino
Paolo Frasca: Univ. Grenoble Alpes, CNRS, Inria
Raoul Prisant: Univ. Grenoble Alpes, CNRS, Inria

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 26, 21 pages

Abstract: Abstract The starting point of this work is a well-known class of linear systems on a graph that asymptotically converge to a consensus state. We consider a variation of this dynamics, by modifying some of the states through the nearest integer function: this change sets the dynamics apart from the consensus dynamics. We focus our study on the case in which the underlying graph is a line, which is particularly significant as it exhibits asymptotic behaviors that are far from consensus. In this case, we compute the equilibria of the system and prove convergence of solutions.

Keywords: Discrete states; Equilibria; Discontinuous ordinary differential equations; Opinion dynamics; 93A16; 93D50; 34A36 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02729-x

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