Analysis of a Spatialized Brain-Body-Environment System

The brain-body-environment framework studies adaptive behavior through embodied and situated agents, emphasizing interactions between brains, biomechanics, and environmental 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 dynamics. To address this limitation, we propose a spatially extended approach using partial differential equations (PDEs) for both the brain and body. As a case study, we revisit a previously developed model of a child swinging, now incorporating spatial dynamics. By considering the spatio-temporal properties of the brain and body, we analyze how input location and propagation along a PDE influence behavior. This approach offers new insights into the role of spatial organization in adaptive behavior, bridging the gap between abstract neural models and the physical constraints of embodied systems. Our results highlight the importance of spatial dynamics in understanding brain-body-environment interactions.