How does functional modularity emerge in a multiregional cortex made with repeats of a canonical local circuit architecture? We investigated this question by focusing on neural coding of working memory, a core cognitive function. Here we report a mechanism dubbed "bifurcation in space", and show that its salient signature is spatially localized "critical slowing down" leading to an inverted V-shaped profile of neuronal time constants along the cortical hierarchy during working memory. The phenomenon is confirmed in connectome-based large-scale models of mouse and monkey cortices, offering an experimentally testable prediction to assess whether working memory representation is modular. Many bifurcations in space could explain the emergence of different activity patterns potentially deployed for distinct cognitive functions, This work demonstrates that a distributed mental representation is compatible with functional specificity as a consequence of macroscopic gradients of neurobiological properties across the cortex, suggesting a general principle for understanding brain's modular organization.