Aggregation and clustering of the multi-agent dynamics with density-dependent influence

초록

Motivated by the demographic effects, we propose and analyze a novel opinion dynamics model with density-dependent interactions and a nonlinear communication function reminiscent of the celebrated Hegselmann-Krause (H-K) model. The model also incorporates heterogeneity through intrinsic opinion tendencies, leading to richer dynamics. In the homogeneous case, where all agents share the same intrinsic tendency, the relative dissimilarities between opinions converge to zero and a single cluster forms. In contrast, under heterogeneous tendencies, we prove that multiple clusters emerge together with velocity alignment within each cluster, provided suitable structural conditions on the system parameters. These theoretical findings are further supported by numerical simulations, which offer qualitative insights beyond the analytical results.

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