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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.12420 |
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| _version_ | 1866929607128645632 |
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| author | Amorim, Giovanna Bizyaeva, Anastasia Franci, Alessio Leonard, Naomi Ehrich |
| author_facet | Amorim, Giovanna Bizyaeva, Anastasia Franci, Alessio Leonard, Naomi Ehrich |
| contents | We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resulting heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel, which we design to ensure that only a small (finite) subset of options can be favored over the continuum. We leverage the spatial invariance of the model linearization to design flexible, distributed opinion-forming behaviors using spatiotemporal frequency domain and bifurcation analysis. We illustrate our model's versatility with an application to robotic navigation in crowded spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatially-invariant opinion dynamics on the circle Amorim, Giovanna Bizyaeva, Anastasia Franci, Alessio Leonard, Naomi Ehrich Analysis of PDEs Social and Information Networks We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resulting heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel, which we design to ensure that only a small (finite) subset of options can be favored over the continuum. We leverage the spatial invariance of the model linearization to design flexible, distributed opinion-forming behaviors using spatiotemporal frequency domain and bifurcation analysis. We illustrate our model's versatility with an application to robotic navigation in crowded spaces. |
| title | Spatially-invariant opinion dynamics on the circle |
| topic | Analysis of PDEs Social and Information Networks |
| url | https://arxiv.org/abs/2409.12420 |