Work

A Nonlocal Aggregation–Diffusion Model with Adaptive Perception Kernels for Descriptive Norm Dynamics

Year: 2026

Type: article

Abstract: This paper presents a partial differential equation (PDE)-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through nonlocal perception kernels and external potential fields. Extending classical transport equations, the framework represents opinion popularity as a continuous distribution, enabling direct interactions without Bayesian guessing of beliefs. Using azithromycin and prednisolone as illustrative treatment features from a real-world coronavirus disease 2019 (COVID-19) dataset, the numerical experiments exhibit reduced local perception-to-target discrepancy under target-based updating, redistribution and the formation of a new unimodal density under fact-informed updates with potential guidance, and persistent multiple peaks without target-based fitting or an external potential field. Quantitative evaluation uses population-weighted local perception-to-target Wasserstein distance estimates for the selected treatment dimensions.

Source: Mathematics

DOI: 10.3390/math14203837

Authors: Chao Li, Ilia Derevitskii, Sergey Kovalchuk

Institution: ITMO University

Language: English

Topic: Opinion Dynamics and Social Influence

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Russian Science Foundation