Spatially-invariant opinion dynamics on the circle
<|reference_start|>Spatially-invariant opinion dynamics on the circle: We propose a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of distributed input. Inspired by perceptual decision-making, we develop the theory for options distributed on the circle, representing, e.g., the set of possible heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel. We design the kernel to ensure that decision-making is robust, in the sense that only a finite subset of options can be favored over the continuum. We prove the spatial invariance of the model linearization and use this result to prove an opinion-forming bifurcation in the model with zero input. We then use space and time frequency domain analysis of the model linearization to infer the ultra-sensitive input-output behavior of the nonlinear dynamics with input. We illustrate our model's versatility with a robotic navigation example in crowded spaces.<|reference_end|>
@article{amorim2024spatially-invariant,
    title={Spatially-invariant opinion dynamics on the circle},
    author={Giovanna Amorim, Alessio Franci and Naomi Ehrich Leonard},
    journal={arXiv preprint arXiv:2409.12420},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12420},
    primaryClass={math.AP cs.SI}
}