The brain-body-environment framework studies adaptive be- havior through embodied and situated agents, emphasizing interactions between brains, biomechanics, and environmen- tal dynamics. However, many models often treat the brain as a network of coupled ordinary differential equations (ODEs), neglecting finer spatial properties which can not only increase model complexity but also constrain observable neural dy- namics. To address this limitation, we propose a spatially ex- tended approach using partial differential equations (PDEs) for both the brain and body. As a case study, we revisit a pre- viously developed model of a child swinging, now incorpo- rating spatial dynamics. By considering the spatio-temporal properties of the brain and body, we analyze how input loca- tion and propagation along a PDE influence behavior. This approach offers new insights into the role of spatial organiza- tion in adaptive behavior, bridging the gap between abstract neural models and the physical constraints of embodied sys- tems. Our results highlight the importance of spatial dynam- ics in understanding brain-body-environment interactions.

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