| Abstract: |
| The public opinions in modern information environments are shaped by the interplay between social conformity and environmental exposure. Interactions among individuals promote opinion alignment, while environmental heterogeneity and selective information exposure may reinforce the alignments with their own interests, known as the information cocoon. This work aims at a mathematical description of the underlying mechanisms by combining the opinion dynamics and bounded-confidence interactions with environmentally biased movement. Starting from the particle-level Hegselmann-Krause model and random movements of agents biased by the environment, a nonlocal PDE system under the mean-field scaling is derived, where opinion transport is driven by consensus dynamics and modulated by an attention-dependent cross-diffusion mechanism. The stability of spatially homogeneous states is analyzed, and the threshold conditions that characterize the phase transition between dispersed and aggregated opinion distributions are proposed. The theoretical results are supported by our numerical results produced by a structure-preserving third-order numerical scheme. Moreover, it demonstrates that the formation of spatial opinion clusters enhances the group consensus, and the environmental information flow may modify the timing and the pathway through which consensus is triggered. These observations provide a quantitative framework for understanding how social conformity and environmental exposure jointly shape the organization of public opinion. |
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