FJ-MM: The Friedkin-Johnsen Opinion Dynamics Model with Memory and Higher-Order Neighbors

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Hauptverfasser: Raineri, Roberta, Zino, Lorenzo, Proskurnikov, Anton
Format: Preprint
Veröffentlicht: 2025
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author Raineri, Roberta
Zino, Lorenzo
Proskurnikov, Anton
author_facet Raineri, Roberta
Zino, Lorenzo
Proskurnikov, Anton
contents The Friedkin-Johnsen (FJ) model has been extensively explored and validated, spanning applications in social science, systems and control, game theory, and algorithmic research. In this paper, we introduce an advanced generalization of the FJ model, termed FJ-MM which incorporates both memory effects and multi-hop (higher-order neighbor) influence. This formulation allows agents to naturally incorporate both current and previous opinions at each iteration stage. Our numerical results demonstrate that incorporating memory and multi-hop influence significantly reshapes the opinion landscape; for example, the final opinion profile can exhibit reduced polarization. We analyze the stability and equilibrium properties of the FJ-MM model, showing that these properties can be reduced to those of a comparison model--namely, the standard FJ model with a modified influence matrix. This reduction enables us to leverage established stability results from FJ dynamics. Additionally, we examine the convergence rate of the FJ-MM model and demonstrate that, as can be expected, the time lags introduced by memory and higher-order neighbor influences result in slower convergence.
format Preprint
id arxiv_https___arxiv_org_abs_2504_06731
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle FJ-MM: The Friedkin-Johnsen Opinion Dynamics Model with Memory and Higher-Order Neighbors
Raineri, Roberta
Zino, Lorenzo
Proskurnikov, Anton
Systems and Control
Multiagent Systems
Optimization and Control
Physics and Society
The Friedkin-Johnsen (FJ) model has been extensively explored and validated, spanning applications in social science, systems and control, game theory, and algorithmic research. In this paper, we introduce an advanced generalization of the FJ model, termed FJ-MM which incorporates both memory effects and multi-hop (higher-order neighbor) influence. This formulation allows agents to naturally incorporate both current and previous opinions at each iteration stage. Our numerical results demonstrate that incorporating memory and multi-hop influence significantly reshapes the opinion landscape; for example, the final opinion profile can exhibit reduced polarization. We analyze the stability and equilibrium properties of the FJ-MM model, showing that these properties can be reduced to those of a comparison model--namely, the standard FJ model with a modified influence matrix. This reduction enables us to leverage established stability results from FJ dynamics. Additionally, we examine the convergence rate of the FJ-MM model and demonstrate that, as can be expected, the time lags introduced by memory and higher-order neighbor influences result in slower convergence.
title FJ-MM: The Friedkin-Johnsen Opinion Dynamics Model with Memory and Higher-Order Neighbors
topic Systems and Control
Multiagent Systems
Optimization and Control
Physics and Society
url https://arxiv.org/abs/2504.06731